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  • A sample of an ideal gas with a molar mass of 0.03 kg/mol is initially at a pressure of 4 atm and a volume of <img alt="0.06 \mathrm{~m}^3" src="https://entrancecorner.oncodecogs.com/gif.latex?0.06

A sample of an ideal gas with a molar mass of 0.03 kg/mol is initially at a pressure of 4 atm and a volume of 0.06 \mathrm{~m}^3 . The gas undergoes an isochoric process during which it absorbs 200 J of heat. Calculate the change in internal energy and the final temperature of the gas.
Given that the gas constant R = 8.314 J/mol · K and the number of moles of gas n = 0.02 mol.

Option: 1

8.314J/mol


Option: 2

18.30 J/mol


Option: 3

45.1 J/mol


Option: 4

5.20 J/mol


Answers (1)

best_answer

The change in internal energy of a gas can be calculated using the first law of thermodynamics:

\mathrm{\Delta U=Q+W}

Where ?U is the change in internal energy, Q is the heat added or removed, and W is the work done. In an isochoric process, no work is done (W = 0), so \DeltaU = Q.
Given that Q = 200 J, we can calculate \DeltaU:

\DeltaU = 200 J

Next, we can use the ideal gas law to calculate the final temperature \mathrm{T_2}

\mathrm{P_1 V_1=n R T_2}

Solving for \mathrm{T_2}:

\mathrm{T_2=\frac{P_1 V_1}{n R}}

Substitute the given values

\mathrm{P_1=4 \mathrm{~atm} \text { (convert to Pascals), } V_1=0.06 \mathrm{~m}^3, n=0.02 \mathrm{~mol}}

\mathrm{R =8.314 J/mol}

Therefore, the correct option is 1.

Posted by

Gautam harsolia

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