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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A class of 10 students taking an exam has a power output per student of about 200 W. Assume the initial temperature of the room is 20°C and that its dimensions are 6.0 m by 15.0 m by 3.0 m. What is the temperature of the room at the end of 1.0 h if all the energy remains in the air in the room and none is added by an outside source? The specific heat of air is 837 J/kg · °C, and its density is about 1.3 × 10−3 g/cm3.

To determine
Temperature of the room at the end of 1.0 h.

Explanation

Section1:

To determine: The energy added to air in one hour.

Answer: Energy added is 7.20×106J

Explanation:

Given Info: Power output per student is about 200 W, time is 1.0 h.

200 W of power is added by each student, So total power is the sum of

10 students.

Formula to calculate total power is,

Ptot=10Peach

  • Ptot is total power output.
  • Peach is power output by each student,

Formula to calculate the power output is,

Q=Ptott

  • Q is heat added to the room,
  • Ptot is total power output,
  • t is the time,

Use 10Peach for Ptot to rewrite the above equation.

Q=10Peacht

Substitute 200 W for Peach , 1.0 h for t  to find Q.

Q=10(200W)(1.0h)(3600s1.0h)=7.20×106J

Thus, the energy added to the air in one hour is 7.20×106J

Section 2:

To determine: To determine the mass of air in the room.

Answer: mass of the air is 351kg

Explanation:

Given Info: Length of the room is 6.0 m, breadth of the room is 15.0 m and height of the room is 3.0 m.

Formula to calculate the volume of the room is,

Vroom=lbh

  • Vroom is volume of the room,
  • l is the length of the room,
  • b is the breadth of the room,
  • h is the height of the room,

Formula to calculate the mass of the air is,

m=ρVroom

  • m is the mass air in the room,
  • ρ is the density of the air,

Use lbh in the above equation to rewrite m.

m=ρlbh

Substitute 1.3kg/m3 for ρ , 6.0 m for l, 15.0 m for b, 3.0 m for h to find m.

m=(1.3kg/m3)(6

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