   Chapter 17, Problem 48P

Chapter
Section
Textbook Problem

An office worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20.°C to 100. °C in 4.00 minutes. The heater is a Nichrome resistance wire connected to a 120-V power supply. Assume the wire is at 100. °C throughout the 4.00-min time interval. (a) Calculate the average power required to warm the water to 100. °C in 4.00 min. (b) Calculate the required resistance in the heating element at 100. °C. (c) Calculate the resistance of the heating element at 20. °C. (d) Derive a relationship between the diameter of the wire, the resistivity at 20. °C, ρ0, the resistance at 20. °C, R0, and the length L. (e) If L = 3.00 m, what is the diameter of the wire?

(a)

To determine
The average power required to warm the water.

Explanation

Given Info: 250.0g of water is heated from 20.0°C to 100.0°C in 4 minutes. The heater with nichrome resistor is connected to 120V supply, 250.0g of water is heated from 20.0°C to 100.0°C in 4 minutes. The heater with nichrome resistor is connected to 120V supply

Explanation:

Formula to calculate the energy required to warm the water is,

E=mc(T2T1)

• E is the heat energy required to warm the water from temperature T1 to T2 ,
• m is the mass of water,
• c is the specific heat capacity of water,

Substitute 250.0g for m , 4186J(kg°C)1 for c , 100.0°C for T2 and 20.0°C for T1 in the above equation to find E

E=(250.0g)(1kg1000g)(4186J(kg°C)-1)(100

(b)

To determine
The resistance of nichrome at 100.0°C

(c)

To determine
The resistance of nichrome at 20.0°C

(d)

To determine
The relationship between resistivity at 20.0°C , diameter of wire, resistance at 20.0°C and length of wire.

(e)

To determine
The diameter of nichrome wire.

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