A 1.50-kg iron horseshoe initially at 680°C is dropped into a bucket containing 19.5 kg of water at 21.0°C. What is the final temperature of the water–horseshoe system? Ignore the heat capacity of the container and assume a negligible amount of water boils away. The water will gain the energy lost by the iron. Using the expressions for the quantity of heat exchanged by the two materials, the change in water temperature can be found. The specific heat of iron is 448 J/kg·°C and the specific heat of water is 4,186 J/kg·°C. We assume that the water–horseshoe system is thermally isolated (insulated) from the environment for the short time required for the horseshoe to cool off and the water to warm up. Then the total energy input from the surroundings is zero, as expressed by the equation Qiron + Qwater  =  0. The energy Q transferred between a sample of mass m of a material and its surroundings with a temperature change ΔT is given by Q  =  mcΔT. Substituting the expressions for iron and water into the energy equation, we have (mcΔT)iron + (mcΔT)water  =  0 or, with T as the final temperature of both the iron and the water, mironciron   T −  °C   + mwatercwater   T −  °C    =  0. Note that the first term in this equation results in a negative number of joules, representing energy lost by the originally hot horseshoe, and the second term is a positive number with the same absolute value, representing energy gained in heat by the colder water.

Question

A 1.50-kg iron horseshoe initially at 680°C is dropped into a bucket containing 19.5 kg of water at 21.0°C. What is the final temperature of the water–horseshoe system? Ignore the heat capacity of the container and assume a negligible amount of water boils away.

The water will gain the energy lost by the iron. Using the expressions for the quantity of heat exchanged by the two materials, the change in water temperature can be found. The specific heat of iron is 448 J/kg·°C and the specific heat of water is 4,186 J/kg·°C.

We assume that the water–horseshoe system is thermally isolated (insulated) from the environment for the short time required for the horseshoe to cool off and the water to warm up. Then the total energy input from the surroundings is zero, as expressed by the equation

Qiron + Qwater  =  0.

The energy Q transferred between a sample of mass m of a material and its surroundings with a temperature change ΔT is given by

Q  =  mcΔT.

Substituting the expressions for iron and water into the energy equation, we have

(mcΔT)iron + (mcΔT)water  =  0

or, with T as the final temperature of both the iron and the water,

mironciron 
 
T −  °C
 
 + mwatercwater 
 
T −  °C
 
 =  0.

Note that the first term in this equation results in a negative number of joules, representing energy lost by the originally hot horseshoe, and the second term is a positive number with the same absolute value, representing energy gained in heat by the colder water.

Expert Answer

1 Rating

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Science
Physics

Thermodynamics

Related Physics Q&A

Find answers to questions asked by students like you.

Q: What speed must a particle attain before its kinetic energy is double the value predicted by the non...

A: Kinetic energy of relativistic particle can be expressed as KER=E-E0=γE0-E0=γ-1E0=γ-1mc2

Q: T3 7.) A basketball of mass 0.6kg is dropped from rest. Just before striking the floor, it has a mom...

A: Click to see the answer

Q: Ticker Tape Diagram Case A Case B Greatest velocity change? Greatest acceleration? Greatest momentum...

A: Click to see the answer

Q: ils of a solenoid of length 0.130 m carry a current of 95.0 A, it produces a magnetic field of 7.00 ...

A: Click to see the answer

Q: Three objects of equal mass  m1 = m2 = m3 = 2.50 kg  are located on the vertices of an equilateral t...

A: Click to see the answer

Q: A layer of oil (n=1.45) floats on an unknown liquid. A ray of light originates in the oil and passes...

A: Apply snells law  n1 sin i = n2 sinr

Q: Two point masses 3 kg and 5 kg are at 4 m and 8 m from the origin on x-axis. Locate the position of ...

A: From the origin, if m1 is at a distance r1 and m2 is at a distance r2 then the center of mass of the...

Q: A helicopter lifts a 100kg crate straight up via cable, with an acceleration of 0.8m/s2. If the crat...

A: Solution: given that mass of crate m = 100 kg a = 0.8 m/s2 d = 5m

Q: What is the voltage at the location of a 0.0001C charge that has an electric potential energy of 0.5...

A: Click to see the answer

Q: A box is pressed against a horizontal spring, compressing the spring from its relaxed length. The bo...

A: Solution: as given K = spring constant of spring X = distance the spring is compressed M = mass box ...

Q: what is the power of a crane that lifts it uniformly in a hurry to a height of 5 meters during 5 sec...

A: The work done is calculated as, W=mghW=200×9.8×5W=9800 J

Q: A traffic light weighing 122 N hangs from a cable tied to two other cablesfastened to a support. The...

A: Click to see the answer

Q: The Bohr model of the single-electron, many-proton ion predicts the emitted/absorbed photon waveleng...

A: Solution:

Q: A particle r = (2t3 + 3t) i + (4 - 5t2) j - t4 k given time-dependent positionIt moves with the vect...

A: Solution: As given that r = (2t3 + 3t) i + (4 - 5t2) j - t4 k

Q: After two time constants, what percentage of the final voltage, emf, is on an initially uncharged ca...

A: After two time constants, the change in final voltage, emf is to be determined.

Q: A spaceship is moving away from Earth at 0.812c when it fires a small rocket in the forward directio...

A: Given data: Speed of space ship with respect to earth, vSE=0.812c Speed of rocket with respect to th...

Q: A wire is drawn through a die, stretching it to four times its original length. By what factor does ...

A: Given, Considering the original length of the wire as L, and new length as L1, L1=4L.

Q: A falling package with a parachute is greatly affected by air resistance. Suppose a package (m = 25 ...

A: Given data: Mass of package is, m=25 kg. The altitude is of, y=1500 m. The speed is, v=45 m/s.

Q: What is the ideal speed to take a 95 m radius curve banked at a 20.0° angle?

A: Maximum speed of car on banked curve is as follows: vmax=rgtanθ                                     ...

Q: If two different forces can accelerate the same block from rest to the same final speed, then the po...

A: Given, Two forces accelerated a block from rest to a final speed 

Q: A charge of 2 micro-C is located inside the sphere of radius 2 m. Find the density of the electric f...

A: Click to see the answer

Q: R=76 A hall has a volume of 5600 m3 and reverberation time of 1.28 sec. If (290 + R) cushioned chair...

A: Click to see the answer

Q: A 0.96N ball A, and a 1.2N ball B connected by stretched spring of negligible mass. When both balls ...

A: Force in the spring is “ K X “ where K is the spring constant and ‘X’ is the extension  or the compr...

Q: An electric eel can generate a 200V, .2 A shock for stunning its prey. What is the eel's power putpu...

A: To found the power output of an electric eel

Q: A flywheel with a diameter of 2.18 m is rotating at an angular speed of 197 rev/min. (a) What is the...

A: Click to see the answer

Q: Light hits an air-glass boundary with an angle of incidence of 62∘. What is the angle of refraction ...

A: When light incident from the air to a medium then the refractive index can be found using Snell's la...

Q: A circular curve of highway is designed for traffic moving at60 km/h. Assume the traffic consists of...

A: For the speed v=60 km/h=60×518=16.66m/s R=150 m (a) For banking angle tanθ=v2rg Substituting the val...

Q: If I am given a problem that provides the weight of a car and its inclination from the ground, how d...

A: Let the mass of the car = m weight of the car = mg W = mg Number of tires = 4 Angle of inclination f...

Q: A person with body resistance between his hands of 10.0 k Ω accidentally grasps the terminals of a 2...

A: a. the circuit diagram to represent the situation is shown below.

Q: A tuning fork that vibrates at a frequency 680 Hz is placed over an 80 centimeter long cylinder that...

A: Click to see the answer

Q: Let's begin with a simple calculation of the weight of air using density. Find the mass of air and i...

A: Given data The length of the room is l = 4.4 m. The width of the room is w = 6.1  m. The height of ...

Q: (a) A large rotating flywheel uniformly increases in angular speed from rest to 0.210 rev/s in 26.0 ...

A: a. in rotational mechanics, equation of motion for the given case can be expressed as ω=ω0+αt

Q: The motion of a jet plane just after landing on a runway is described by the a-t graph. Determine th...

A: Click to see the answer

Q: A person swings a rock around on a string, causing it to sweep out in a circle of radius 0.53 m. If ...

A: For the given case, Acceleration experience by rock due to uniform circular motion is known as centr...

Q: An electronic device designed to operate at any temperature in the range from –10.0ºC to 55.0ºC cont...

A: Pure carbon resistors have temperature coefficient of resistivity of α=-0.5×10-3 /Co Given temperatu...

Q: Two men pushing a stalled car generate a net force of 840 N for 5.0 s. What is the magnitude of the ...

A: Force is equal to rate of change of momentum.  The initial momentum is zero since it is stalled.   

Q: Starting from rest, a person pedals a bicycle such that the angular acceleration of the wheels is a ...

A:                        Speed =Distance Time                    Velocity =DisplacementTime           ...

Q: A beam resting on two pivots has a length of L = 6.00 m and mass M = 92.0 kg.The pivot under the lef...

A: (a) Condition for rotational equilibrium τnet=0n2l-mgx-MgL2=0n2=mgx+MgL2l

Q: A toroid has 1430 turns of a large diameter wire carrying a current of 10.8 kA. The inner and outer ...

A: The given values are, N=1430I=10.8 kA=10.8×103 Ari=0.600 mro=1.20 m

Q: Verify that the units of a volt-ampere are watts, as implied by the equation P = IV .

A: The unit of power =W (Watt) Unit of current =A (Ampere) Unit of voltage =V (Volts)

Q: A helicopter lifts a 100kg crate straight up via cable, with an acceleration of 0.8m/s2. If the crat...

A: Given: The mass of the crate is m=100 kg, The acceleration is a=0.8 m/s2, The total lifted distance...

Q: (a) What is the efficiency of an out-of-condition professor who does 2.30 ✕ 105 J of useful work whi...

A: Click to see the answer

Q: Semi-trailer trucks have an odometer on one hub of a trailer wheel. The hub is weighted so that it d...

A: Diameter of the wheel is d = 1.14 m Number of revolutions is n = 150000 So, perimeter (S) of the whe...

Q: Derive the FARADAYS LAW AND LENZS LAW in term of magnetic field? you have to prove both laws for a c...

A: Faraday's Law of electromagnetic induction Whenever there is a change in magnetic flux linked to a ...