Question

$2kg$ of air is heated at constant volume. The temperature of the air has increased from $293K$ to $313K$. If the specific heat of air at constant volume is $0.718KJ/kgK$, the amount of heat absorbed in $kJ$ and $kcal$ is $\left( {J = 4.2/kcal} \right)$
A. \[6.838kJ\]
B. $7.8kJ$
C. $14.68kJ$
D. $28.72kJ$

Answer 1

Hint: To solve this question, we need to use the formula for the heat absorbed in the constant volume process. Substituting the values of the mass of air, specific heat at constant volume, and the change in temperature from the information given in the question, we can get the final answer.

Formula used: The formula used to solve this question is given by
$Q = m{C_V}\Delta T$, here $Q$ is the amount of heat absorbed or rejected by $m$ mass of a substance having the specific heat at constant volume of ${C_V}$ when it is subjected to a change in the temperature of $\Delta T$.

Complete step by step answer:
According to the question, we have a constant volume process in which a given amount of air is heated. We know that the heat exchanged by a substance in a constant volume process is given by
$Q = m{C_V}\Delta T$
$ \Rightarrow Q = m{C_V}\left( {{T_2} - {T_1}} \right)$
Now, according to the question we have the mass of air equal to $2kg$, the specific heat capacity at constant volume of air is equal to $0.718KJ/kgK$. Also, the initial temperature of air is equal to $293K$ and its final temperature is equal to $313K$. Therefore substituting \[m = 2kg\], \[{C_V} = 0.718KJ/kgK\], ${T_1} = 293K$, and ${T_2} = 313K$ in the above equation, we get
$ \Rightarrow Q = 2 \times 0.718 \times \left( {313 - 293} \right)$
On solving we get
$ \Rightarrow Q = 28.72kJ$
Thus, the heat absorbed by the air is equal to $28.72kJ$.
Hence, the correct answer is option D.

Note: Do not convert the given value of the specific heat capacity at constant volume into its SI unit, that is, from $KJ/kgK$ to $J/kgK$. This is because we are asked to find out the amount of heat absorbed in kilo-joules. So directly substituting the value of the heat capacity in the formula, we got the heat absorbed in kilo-joules.