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Chapter 19: Q50P (page 580)

We give70鈥�Jas heat to a diatomic gas, which then expands at constant pressure. The gas molecules rotate but do not oscillate. By how much does the internal energy of the gas increase?

Short Answer

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Step by step solution

01

Given data

Heat energy given to a diatomic gas isQ=70J

02

Understanding the concept

The expression for the amount of energy transferred to the gas is given by,

Q=nCV螖T

Here Q is the amount of energy transferred to gas,n is the number of moles, Cvis the specific heat capacity at constant volume and 螖Tis the temperature difference.

03

Calculate by how much the internal energy of the gas increases

螖Eint=nCV螖T

But, for diatomic gas,CV=52R

Hence,

螖Eint=52nR螖T 鈥︹�� (i)

Also,Q=nCP螖T

But, for diatomic gasCP=72R

Hence,

Q=72nR螖TnR螖T=27Q

Substitute27Qfor nR螖Tinto the equation (i)

螖Eint=5227Q

Substitute70鈥�J for Q into the above equation,

鈬�螖Eint=50鈥塉

Therefore, the increase in the internal energy is50J.

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Most popular questions from this chapter

Question: Container A in figure holds an ideal gas at a pressure of 5.0脳105Paand a temperature of 300 kIt is connected by a thin tube (and a closed valve) to container B, with four times the volume of A. Container B holds the same ideal gas at a pressure of 1.0脳105Paand a temperature of 400 k. The valve is opened to allow the pressures to equalize, but the temperature of each container is maintained. What then is the pressure?

In the p-V diagram of Fig.19鈭�17, the gas does5Jof work when taken along isotherm ab and 4Jwhen taken along adiabatic. What is the change in the internal energy of the gas when it is taken along the straight path from a to c?

One mole of an ideal diatomic gas goes from a to c along the diagonal path in figure. The scale of the vertical axis is set bypab=5.0鈥�kPaand pc=2.0鈥�kPa, and the scale of the horizontal axis is set by Vbc=4.0m3andVa=2.0鈥�m3. During the transition,

a) What is the change in internal energy of the gas

b) How much energy is added to the gas as heat?

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Suppose 12.0gof oxygen (O2) gas is heated at constant atmospheric pressure from25.0鈭�Cto125.0鈭�Cto.

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