Question 793: Thermodynamics & KTG

Question

A monoatomic gas is heated at constant pressure. The percentage of total heat used for doing external work is

Accepted Answer

For a monoatomic gas, when heated at constant pressure, the heat added to the system can be used to do work and to change the internal energy.
The specific heat at constant pressure is related to the specific heat at constant volume by:
$$ C_p = C_v + R $$
where $ R $ is the ideal gas constant. For a monoatomic gas, $ C_v = \frac{3}{2}R $, so:
$$ C_p = \frac{3}{2}R + R = \frac{5}{2}R $$
The work done by the gas during expansion at constant pressure can be represented by:
$$ W = P \Delta V = nR \Delta T $$
The total heat supplied at constant pressure is:
$$ Q = nC_p \Delta T = n \left( \frac{5}{2} R ight) \Delta T $$
The percentage of heat used to do work is given by the ratio:
$$ 	ext{Percentage of heat used for work} = \frac{W}{Q} 	imes 100 = \frac{nR \Delta T}{n \left( \frac{5}{2} R ight) \Delta T} 	imes 100 $$
This simplifies to:
$$ \frac{2}{5} 	imes 100 = 40\% $$
Thus, the percentage of total heat used for doing external work is
40%
.
Option B (40%) is the correct answer.

Answer

30%

Answer

40%

Answer

50%

Answer

60%

Thermodynamics & KTG

A monoatomic gas is heated at constant pressure. The percentage of total heat used for doing external work is

Choose the correct answer: