HC Verma - Concepts of Physics Part 2

Book: HC Verma - Concepts of Physics Part 2

Chapter: 27. Specific Heat Capacities of Gases

Subject: Physics - Class 12th

Q. No. 5 of Objective I

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5

70 calories of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is


We know that, Q = nCpdT… (i),


Where


Q = heat required to raise the temperature


n = number of moles


Cp = specific heat capacity at constant pressure


dT = rise in temperature.


In this first case,


Amount of heat required(Q) = 70 cal


Number of moles(n) = 2 mol


Rise in temperature(dT) = (35-30)0C = 50C


Hence, from (i), we get Cp = 7 calmol-1 0C-1


Now, we know, Cp - Cv = R,


Where


Cp = specific heat capacity at constant pressure


Cv = specific heat capacity at constant volume


R = universal gas constant = 1.98 calmol-1 0C-1


Therefore, we get Cv = Cp - R = (7-1.98) cal mol-1 0C-1


= 5.02 cal mol-1 0C-1


Now, in the new case, change in temperature dT = 50C as before. Number of moles(n) = 2, and Cv = 5.02 calmol-1 0C-1


Hence, amount of heat required to raise the temperature of the same gas through the same range


dQ = nCvdT = (2 x 5.02 x 5) cal = 50.2 cal which is approximately equal to 50 cal.


Hence, the correct option is (b).

Chapter Exercises

Short Answer
Objective I
Objective II
Exercises

More Exercise Questions

1

Work done by a sample of an ideal gas in a process A is double the work done in another process B. The temperature rises through the same amount in the two processes. If CA and CB be the molar heat capacities for the two processes.
2

For a solid with a small expansion coefficient,
3

The value of CP – CV is 1.00 R for a gas sample in state A and is 1.08R in state B. Let PA, PB denote the pressures and TA, and TB denote the temperatures of the states A and B respectively. Most likely
4

Let CV and CP denote the molar heat capacities of an ideal gas at constant volume and constant pressure respectively. Which of the following is a universal constant?
5

70 calories of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is
6

The molar heat capacity for the process shown in the figure is
7

The molar heat capacity for the process shown in the figure is
8

In an isothermal process on an ideal gas, the pressure increases by 0.5%. The volume decreases by about
9

In an adiabatic process on gas with γ = 1.4, the pressure is increased by 0.5%. The volume decreases by about
10

Two samples A and B are initially kept in the same state. Sample A is expanded through an adiabatic process and sample B through an isothermal process. The final volumes of the samples are the same. The final pressures in A and B are pA and PB respectively.
11

Let Ta and Tb be the final temperatures of the samples A and B respectively in the previous question.
12

Let ΔWa and ΔWb be the work done by the systems A and B respectively in the previous question.
13

The molar heat capacity of oxygen gas at STP is nearly 2.5R. As the temperature is increased, it gradually increases and approaches 3.5R. The most appropriate reason for this behaviour is that at high temperatures.

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