In a cylinder, 2 . 0 moles of an ideal monatomic gas initially at 1 . 0 × 10 6 Pa and 300 K expands until its volume doubles. Compute the work done if the expansion is isothermal

Given that cylinder contains 2 . 0 moles of ideal monoatomic gas. Initial pressure is 1 . 0 × 10 6 Pa . Initial temperature is 300 K . Gas is expanded untill its volume doubles.We are suppose to find out the work done if expansion is isothermal. Let P 1 = 1 × 10 6 Pa = 10 6 N / m 2 ; T 1 = 300 K ; n = 2 mOles. Final volume = 2 (initial volume) ⇒ V 2 = 2 V 1 W isothermal = 2 . 303 n R T log V 2 / V 1 ⇒ W = 2 . 303 × 2 × 8 . 3 × 300 log 2 W = 3452 J Thus work done in isothermal expansion will be 3452 J .

In a cylinder, 2 . 0 moles of an ideal monatomic gas initially at 1 . 0 × 10 6 Pa and 300 K expands until its volume doubles. Compute the work done if the expansion is adiabatic?

Let P 1 = 1 × 10 6 Pa = 10 6 N / m 2 ; T 1 = 300 K ; n = 2 moles. Final volume = 2 (initial volume) ⇒ V 2 = 2 V 1 W adiabatic = n R T 1 - T 2 γ - 1 For adiabatic process: T 1 V 1 γ - 1 = T 2 V 2 γ - 1 T 2 = T 1 V 1 V 2 γ - 1 = 300 × 1 2 5 / 3 - 1 ⇒ T 2 = 189 K W = n R T 1 - T 2 γ - 1 = 2 × 8 . 3 × 300 - 189 5 / 3 - 1 ⇒ W = 2764 J Thus work done is 2764 J .

In a cylinder, 2 . 0 moles of an ideal monatomic gas initially at 1 . 0 × 10 6 Pa and 300 K expands until its volume doubles. Compute the work done if the expansion is isobaric.

It is said in the question that 2 . 0 moles of ideal monoatomic gas expands untill its volume doubles. Pressure given is 1 . 0 × 10 6 Pa . We are supposed to find out work done if expansion is isobaric. Let P 1 = 1 × 10 6 Pa = 10 6 N / m 2 ; T 1 = 300 K ; n = 2 moles. Final volume = 2 (initial volume) ⇒ V 2 = 2 V 1 W isobaric = P V 2 - V 1 ⇒ P 1 V 1 = n R T 1 V 1 = n R T 1 P 1 = 2 × 8 . 3 × 300 10 6 ⇒ V 1 = 4 . 98 × 10 - 3 m 3 W = P V 2 - V 1 = P 2 V 1 - V 1 = P V 1 ⇒ W = 10 6 × 4 . 98 × 10 - 3 J ⇒ W = 4980 J Thus work done is 4890 J

E M B I B E

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 4 - Thermodynamics>ILLUSTRATIONS

B M Sharma Solutions for Chapter: Thermodynamics, Exercise 1: ILLUSTRATIONS

Author:B M Sharma

B M Sharma Physics Solutions for Exercise - B M Sharma Solutions for Chapter: Thermodynamics, Exercise 1: ILLUSTRATIONS

Attempt the free practice questions on Chapter 4: Thermodynamics, Exercise 1: ILLUSTRATIONS with hints and solutions to strengthen your understanding. PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS solutions are prepared by Experienced Embibe Experts.

Questions from B M Sharma Solutions for Chapter: Thermodynamics, Exercise 1: ILLUSTRATIONS with Hints & Solutions

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IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 4 - Thermodynamics>ILLUSTRATIONS>Q 4.23

In a cylinder, $2.0$ moles of an ideal monatomic gas initially at $1.0 \times 10^{6} Pa$ and $300 K$ expands until its volume doubles. Compute the work done if the expansion is isothermal

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 4 - Thermodynamics>ILLUSTRATIONS>Q 4.23

In a cylinder, $2.0$ moles of an ideal monatomic gas initially at $1.0 \times 10^{6} Pa$ and $300 K$ expands until its volume doubles. Compute the work done if the expansion is adiabatic?

MEDIUM

Physics

IMPORTANT

PHYSICS FOR JOINT ENTRANCE EXAMINATION WAVES AND THERMODYNAMICS>Chapter 4 - Thermodynamics>ILLUSTRATIONS>Q 4.23

In a cylinder, $2.0$ moles of an ideal monatomic gas initially at $1.0 \times 10^{6} Pa$ and $300 K$ expands until its volume doubles. Compute the work done if the expansion is isobaric.

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