Question

A sample of air weighing 1.18 g occupies $1.0\times {10}^{3}c{m}^3$ When kept at 300 K and $1.0\times {10}^3$ Pa. When 2.0 cal of heat is added to it at constant volume, its temperature increases by $1^{0}C$. Calculate the amount of heat needed to increase the rtemperature of air by $1^{0}C$ at constant pressure if the mechanical equivalent of heat is $4.2\times {10}^{-7}ergca{l}^{-1}.$ Assume that air hehaves as an ideal gas.

Answer 1

m = 1.18 g

V = $1\times {10}^{8}c{m}^8=1L$

T = 300 K, P = ${10}^5$ Pa

PV = nRT

or n = $\frac{PV}{RT}[{10}^5$ Pa = 1~atm]

$\Rightarrow n=\frac{1}{8.2\times {10}^{-2}\times 3\times {10}^2}$

$\Rightarrow$ = $\frac{1}{8.2\times 3}=\frac{1}{24.6}$

Now, $C_v$ = $\frac{1}{n}\times 2=24.6\times 2$ = 49.2

$C_p=R+C_v$ =1.987 + 49.2

= 51.187

Q = $n{C}_p$ dT

= $\frac{1}{24.6}\times 51.187\times 1$

= 2.08 cal