Question

Find the change in internal energy in joulewhen 10$g$ of air is heated from ${30}^{\circ }C$ to ${40}^{\circ }C$

• A. 62.24$J$
• B. 72.24$J$
• C. 52.24$J$
• D. 82.24$J$

Answer 1

The correct option is B 72.24$J$

Given$,$

Mass of air $=10g$

Since $1g=1\times {10}^{-3}kg$

So$,$ $10g=10\times {10}^{-3}kg$

mass of air $= 10 \times {10^{ - 3}} kg$

Air is heated from $30c$ to $40c$

We know$,$

$0°C+273.15=273.15K$,i.e.,$

$30°C$ in Kelvin $=30+273.15=303K$

$40°C$ in Kelvin $=40+273.15=313K$

So $,$

$\Delta T=313-303K=10K$

We know$,$

$=0.172kcal/kgK$ and

$J=4200J/k.cal$

Now$,$

Change in internal energy $=m\times c_v\times \times \Delta T$

$=10\times {10}^3\times 0.172\times 4.2\times 10³\times 10$

$=17.2\times 4.2$

$=72.24J$

Hence,

option $\left(B\right)$ is correct answer.