Question
A system containing one mole of an ideal gas is expanded adiabatically. If the temperature falls from T1 to T2, find the work done by the gas.
✓
Answer
W.D. in adiabatic process $\text{W}=\frac{1}{1-\text{r}}[\text{P}_2\text{V}_2-\text{P}_1\text{V}_1]$
If T2 is final temperature of gas in adiabatic expansion, then from standard eq.
$\text{P}_1\text{V}_1=\text{RT}_1$ and $\text{P}_2\text{V}_2=\text{RT}_2$
Putting there values, we have,
$\text{W}=\frac{1}{1-\text{r}}[\text{RT}_2-\text{RT}_1]=\frac{\text{R}(\text{T}_1-\text{T}_2)}{1-\text{r}}$
If T2 is final temperature of gas in adiabatic expansion, then from standard eq.
$\text{P}_1\text{V}_1=\text{RT}_1$ and $\text{P}_2\text{V}_2=\text{RT}_2$
Putting there values, we have,
$\text{W}=\frac{1}{1-\text{r}}[\text{RT}_2-\text{RT}_1]=\frac{\text{R}(\text{T}_1-\text{T}_2)}{1-\text{r}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
It is heard sometime that mercury is used in defining the temperature scale because it expands uniformly with temperature. If the temperature scale is not yet defined, is it logical to say that a substance expands uniformly with temperature?
A non-ideal battery is connected to a resistor. Is work done by the battery equal to the thermal energy developed in the resistor? Will your answer change if the battery is ideal?
Calculate the percentage increase in length of a wire of diameter 2.5mm stretched by a force of 100kg weight. Young's modulus of elasticity of wire is 12.5 × 1011 dyne/ sq cm.
A player throws a ball upwards with an initial speed of 29.4m s–1.
What is the direction of acceleration during the upward motion of the ball?
What is the direction of acceleration during the upward motion of the ball?
The force acting on a particle moving along X-axis is F = -k(x - u0t) where k is a positive constant. An observer moving at a constant velocity v0, along the X-axis looks at the particle. What kind of motion does he find for the particle?
The position-time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown in Fig. Choose the correct entries in the brackets below :
(a) (A/B) lives closer to the school than (B/A)
(b) (A/B) starts from the school earlier than (B/A)
(c) (A/B) walks faster than (B/A)
(d) A and B reach home at the (same/different) time
(e) (A/B) overtakes (B/A) on the road (once/twice).
(a) (A/B) lives closer to the school than (B/A)
(b) (A/B) starts from the school earlier than (B/A)
(c) (A/B) walks faster than (B/A)
(d) A and B reach home at the (same/different) time
(e) (A/B) overtakes (B/A) on the road (once/twice).
If two vectors of equal magnitude add to either of them by magnitude, what is the angle between them?
If the co-efficient of performance of a refrigerator is 5 and operates at the room temperature (27°C), find the temperature inside the refrigerator.
Answer the following:
You are given a thread and a metre scale. How will you estimate the diameter of the thread?
You are given a thread and a metre scale. How will you estimate the diameter of the thread?
A curve is represented by $\text{y}=\sin\text{x}.$ If x is changed from $\frac{\pi}{3}$ to $\frac{\pi}{3}+\frac{\pi}{100},$ find approximately the change in y.
→