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  • A 3-mole sample of an ideal monatomic gas is initially at a temperature of 200 K and a volume of 10 liters. The gas undergoes an isochoric process, during which it absorbs 1500 J of heat. If the fi

A 3-mole sample of an ideal monatomic gas is initially at a temperature of 200 K and a volume of 10 liters. The gas undergoes an isochoric process, during which it absorbs 1500 J of heat. If the final temperature of the gas is 400 K, calculate the heat capacity at constant volume \mathrm{(C_v)} for this gas.
 

Given: Initial temperature \mathrm{(T_1)} = 200 K
Initial volume \mathrm{(V_1)} = 10 liters
Heat absorbed(Q) = 1500 J
Final temperature \mathrm{(T_2)} = 400 K
The gas is ideal and monatomic.

Option: 1

5.7 J/K


Option: 2

7.5 J/K


Option: 3

9.0 J/K


Option: 4

10.9 J/K


Answers (1)

best_answer

Step 1: Calculate the change in temperature \mathrm{ (\Delta T)}:

                        \mathrm{\Delta T=T_2-T_1=400 K-200 K=200 K}

Step 2: Calculate the heat capacity at constant volume \mathrm{(C_v)}:
The heat capacity at constant volume \mathrm{(C_v)} is calculated using the formula:

                      \mathrm{C_v=\frac{Q}{\Delta T}}

Substitute the given values:

                         \mathrm{Q=1500 J, \quad \Delta T=200 K}

Calculating the value of \mathrm{C_{v}}:

                         \mathrm{C_v=\frac{1500 \mathrm{~J}}{200 \mathrm{~K}}=7.5 \mathrm{~J} / \mathrm{K}}

Answer: The heat capacity at constant volume \mathrm{(C_v)} for the given monatomic ideal gas is approximately 7.5 J/K.
So, correct option is (2)

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manish

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