Question

A quantity of heat Q is supplied to a monoatomic ideal gas which expands at constant pressure. The fraction of heat that goes into work done by the gas is :

• A. $\frac{2}{5}$
• B. $\frac{5}{2}$
• C. $\frac{4}{5}$
• D. 1

Answer 1

The correct option is A $\frac{2}{5}$

The heat Q is converted into the internal energy and work. According to the first law of thermodynamics,

$Q=U+W$

$n{C}_p\Delta T=n{C}_v\Delta T+W$

The dfraction of heat converted to work is given as $\frac{W}{Q}=\frac{n{C}_p\Delta T-n{C}_v\Delta T}{n{C}_p\Delta T}=\frac{C_p-C_v}{C_p}=\frac{\frac{5}{2}R-\frac{3}{2}R}{\frac{5}{2}R}=\frac{2}{5}$