Question

An ideal gas expands from $100c{m}^{3}to200c{m}^3$ at a constant pressure of $2.0\times {10}^{5}Pawhen50J$ of heat is supplied to it. Calculate

(a) The change in internal energy of the gas

(b) The number of moles in the gas if the initial temperature is 300 K.

(c) The molar heat capacity $C_p$ at constant pressure and

(d) The milar heat capacity $C_v$ at constant volume

Answer 1

$V_1=100c{m}^8,V_2=200c{m}^8,$

P = $2\times {10}^5$ Pa dQ = 50 J

(a) dQ = dU + dW

$\Rightarrow 50=dU+2\times {10}^5$

(200-100) $\times {10}^{-6}$

$\Rightarrow 50=dU+2\times 10$

$\Rightarrow$ dU = 30 J.

(b) 30 = n $\times \frac{3}{2}\times 8.3\times 300$

[U = $\frac{3}{2}$ nRt for monoatimoc ]

$\Rightarrow n=\frac{2}{(83\times 3)}=\frac{2}{249}=0.008$

(c) dU = $n{C}_{v}DT$

$\Rightarrow c_v=\frac{dU}{ndT}=\frac{30}{0.008\times 300}=12.5$

$C_p=c_v+R=12.5+8.3=20.8$

(d) $C_v$ = 12.5