Question

When 100 J of heat is given to an ideal gas it expands from $200c{m}^3$ to $400c{m}^3$ at a constant pressure of $3\times {10}^5$ Pa. Then calculate :$R=[\frac{25}{3}J/mol-k]$ The molar heat capacity $C_p$ at constant pressure when the $T=400K$ is

• A. $\frac{125}{3}J/mol-K$
• B. $\frac{125}{7}J/mol-K$
• C. $\frac{125}{9}J/mol-K$
• D. None of these

Answer 1

The correct option is C $\frac{125}{9}J/mol-K$

For the given information, ideal gas equation can be written as
$PdV=nRdT$
$ndT=\frac{PdV}{R}=\frac{(3\times {10}^5)(400-200)\times {10}^{-6}}{\frac{25}{3}}=\frac{72}{10}$
We have
$C_p=\frac{Q}{ndT}=\frac{100}{\frac{72}{10}}=\frac{125}{9}J/mole-K$
Option C.