Question

One mole of an ideal monatomic gas requires 210 J heat to raise the temperature by 10 K, when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by 10 K then heat required is

• A. 238 J
• B. 126 J
• C. 210 J
• D. 350 J

Answer 1

The correct option is B 126 J

$(△Q{)}_P$ = $\mu C_P△T$ and $(△Q{)}_V$ = $\mu C_V△T$
$\Rightarrow$ $\frac{(△Q{)}_V}{(△Q{)}_P}$ = $\frac{C_v}{C_p}$ = $\frac{\frac{3}{2}R}{\frac{5}{2}R}$ = $\frac{3}{5}$
[$\because$ $(C_V{)}_{mono}=\frac{3}{2}R,(C_P{)}_{mono}=\frac{5}{2}R$]
$\Rightarrow$ $(△Q{)}_V$ = $\frac{3}{5}\times (△Q{)}_P$ = $\frac{3}{5}\times 210=126J$