32 gram of oxygen gas at temperature 27 ° C is compressed adiabatically to 1 3 of its initial volume. Calculate the change in internal energy ( γ = 1 . 5 for oxygen).

For the process to take place adiabatically, we know that internal energy is given as, d U = n C v d T = n R ( γ − 1 ) d T . Now, P V γ = constant . So, we can say that, V γ × n R T V = constant ⇒ T V ( γ − 1 ) = constant . So, we can say, T 1 V 1 ( γ − 1 ) = T 2 V 2 ( γ − 1 ) 300 V 1 ( γ − 1 ) = T 2 V 3 ( γ − 1 ) 300 T 2 = 1 3 1 . 5 - 1 T 2 = 300 1 / 3 = 300 3 K N = number of moles = 32 32 = 1 . Now, the internal energy can be written as, d U = 1 × R ( 1 . 5 − 1 ) × 300 1 . 732 - 1 ⇒ 2 R × 300 3 − 1 = 2 × 25 3 × 300 1 . 732 − 1 = 50 × 100 × 0 . 732 J = 3660 J .

The following figure is given for 1 mole gas. Then, find out net work done in the cyclic process.

In the given figure, for the path B A , work done = n R T ln V A V B = − 200 R ln 2 where, R = 8 . 314 J mol - 1 K - 1 . For path B C , volume is constant as we can see from the graph. Work done will be = P ∆ V = 0 For the path D C , work done, = n R T ln V C V D = 400 R ln 2 Again, in the path A D , volume is constant. So, work done = 0 . Hence, the net work done = 200 R ln 2 . So, on solving, we get 1152 . 6 J .

E M B I B E

Beta Question Bank for Medical: Physics>Chapter 17 - Thermodynamics>BEGINNER'S BOX - 4

Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 4: BEGINNER'S BOX - 4

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Questions from Embibe Experts Solutions for Chapter: Thermodynamics, Exercise 4: BEGINNER'S BOX - 4 with Hints & Solutions

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Beta Question Bank for Medical: Physics>Chapter 17 - Thermodynamics>BEGINNER'S BOX - 4>Q 1

$32 gram$ of oxygen gas at temperature $27 ° C$ is compressed adiabatically to $\frac{1}{3}$ of its initial volume. Calculate the change in internal energy ( $γ = 1.5$ for oxygen).

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Beta Question Bank for Medical: Physics>Chapter 17 - Thermodynamics>BEGINNER'S BOX - 4>Q 5

An ideal gas expands isothermally along $A B$ and does $700 J$ of work.

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(a) How much heat does the gas exchange along $A B$ .

(b) The gas expands adiabatically along $B C$ and does $400 J$ of work. When the gas returns to $A along C A$ , it exhausts $100 J$ of heat to its surroundings. How much work is done on the gas along this path.

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Beta Question Bank for Medical: Physics>Chapter 17 - Thermodynamics>BEGINNER'S BOX - 4>Q 6

For one mole of an ideal gas at $300 K$ occupies a volume of $0.36 m^{3}$ at a pressure of $2 atm$ . The gas expands adiabatically until its volume becomes $1.44 m^{3}$ . Next, the gas is compressed isobarically to its original volume. Finally, the pressure is increased isochorically until the gas returns to as initial state (see figure).