Question

When 18.9 kJ is transferred to a gas sample in a constant volume adiabatic container with a calorimeter constant of 2.22 Kj/K, the temperature of the gas (and the calorimeter) increases by 8.06 K. (a) What is the heat capacity of the sample? (b) If the sample has a mass of 0.5 kilograms, what is the specific heat capacity of the substance? (c) If the sample is Krypton, what is the molar heat capacity at constant volume of Krypton? The molar mass of Krypton is 83.8 grams/mole.

Answer 1

Answer:

(a) Cgas = 0.125 kJ/k

(b) cgas = 0.25kJ/kg.K

(c) cm(gas) = 0.021kJ/mol.K

Explanation:

18.9 kJ is equal to the sum of the heat absorbed by the gas and the heat absorbed by the calorimeter.

Qcal + Qgas = 18.9 kJ  [1]

We can calculate the heat absorbed using the following expression.

Q = C . ΔT

where,

C is the heat capacity

ΔT is the change in the temperature

(a) What is the heat capacity of the sample?

From [1],

Ccal . ΔT + Cgas . ΔT = 18.9 kJ

(2.22kJ/K) × 8.06 K + Cgas × 8.06 K = 18.9 kJ

Cgas = 0.125 kJ/k

(b) If the sample has a mass of 0.5 kilograms, what is the specific heat capacity of the substance?

We can calculate the specific heat capacity (c) using the following expression:

$c=\frac{C}{m} =\frac{0.125kJ/K}{0.5kg} =0.25kJ/kg.K$

(c) If the sample is Krypton, what is the molar heat capacity at constant volume of Krypton? The molar mass of Krypton is 83.8 grams/mole.

The molar heat capacity is:

$\frac{0.25kJ}{kg.K} .\frac{1kg}{1000g} .\frac{83.8g}{mol} =0.021kJ/mol.K$