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

The heat capacity of the sample is 2.34 kJ/K. The specific heat capacity of the substance is 4.68 kJ/(kg*K). The molar heat capacity at constant volume of Krypton is 0.0559 kJ/(mol*K).

Step-by-step explanation:

The heat capacity of a substance is the amount of energy required to increase its temperature by 1 degree. The specific heat capacity is the amount of energy required to increase the temperature of 1 gram of a substance by 1 degree.

(a) To find the heat capacity of the sample, we can use the equation Q = CΔT, where Q is the amount of heat transferred, ΔT is the change in temperature, and C is the heat capacity. Rearranging the equation, C = Q/ΔT. Plugging in the given values, C = 18.9 kJ / 8.06 K

= 2.34 kJ/K.

(b) To find the specific heat capacity of the substance, we need to know the mass of the sample. Given that the mass is 0.5 kilograms, we can use the equation cs = C/m, where cs is the specific heat capacity, C is the heat capacity, and m is the mass. Plugging in the values, cs = 2.34 kJ/K / 0.5 kg

= 4.68 kJ/(kg*K).

(c) To find the molar heat capacity at constant volume of Krypton, we can use the equation Cm = cs / M, where Cm is the molar heat capacity, cs is the specific heat capacity, and M is the molar mass. Plugging in the values, Cm = 4.68 kJ/(kg*K) / 83.8 g/mol

= 0.0559 kJ/(mol*K).

Answer 2

(a) Cgas = 0.125 kJ/k

(b) cgas = 0.25kJ/kg.K

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

Step-by-step 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=(C)/(m) =(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:

`(0.25kJ)/(kg.K) .(1kg)/(1000g) .(83.8g)/(mol) =0.021kJ/mol.K`