Question

The molar specific heat of oxygen at constant pressure ${C_p} = 7.03cal/mol^\circ C$ and$R = 8.32J/mol^\circ C$ . The amount of heat taken by 5 moles of oxygen when heated at constant volume from $10^\circ C$ to $20^\circ C$ will be approximately.
A. 25 cal
B. 50 cal
C. 253 cal
D. 500 cal

Answer 1

Molar heat is that amount of capacity in which heat is needed to raise the temperature of 1 mole of a substance by 1 kelvin or$1^\circ C$ at constant volume. It is the amount of heat energy required per unit temperature. ${C_p} - {C_v} = R$ Here R is the universal gas constant.

Complete answer:
Now from the question
Given ${C_p} = 7.03cal/mol^\circ C$
$R = 8.32J/mol^\circ C = \dfrac{{8.32}}{{4.2}}cal/mol^\circ C$ (since 1calorie=4.2Joule approx)
${T_1} = 10^\circ C$ and ${T_2} = 20^\circ C$
Change in a temperature $\Delta T = {T_2} - {T_1} = 20 - 10 = 10^\circ C$
Molar heat capacity at constant volume,
${C_p} - {C_v} = R$
${C_v} = {C_p} - R$
${C_v} = 7.03cal/mol^\circ C - \dfrac{{8.32}}{{4.2}}cal/mol^\circ C$
${C_v} = 5.05cal/mol^\circ C$ approx
Amount of heat absorbed $\Delta Q = n{C_v}\Delta T$
$= (5 \times 5.05)10cal$
$= 252.5 = 253cal$ approx

So, the correct answer is “Option C”.

Additional Information:
The (cal) calorie is defined as a unit of heat and energy which is equal to the amount of energy that is required to raise the temperature of 1gram of water by $1^\circ C$ .
Molar heat capacity is expressed in units of J/K/mol or J/mol.K, as we know K kelvin is joules and m number of moles. And a less common heat is kilogram-calories (cal). To express heat capacity in terms of pound-mass using temperatures in degree Rankine or Fahrenheit is impossible.

Note:
7.2cal/mol is the molar specific heat of oxygen at constant pressure. The term universal gas constant used in this question is equivalent to the Boltzmann constant, but it expressed in units of energy per temperature increment per mole moreover it is denoted by (R). The (R) calculated from the equation PV=nRT.