A gas takes part in two processes in which it is heated from the … - Vidyadip

MCQ

A gas takes part in two processes in which it is heated from the same initial state $1$ to the same final temperature. The processes are shown on the $P-V$ diagram by the straight line $1-2$ and $1-3$. $2$ and $3$ are the points on the same isothermal curve. $Q_1$ and $Q_2$ are the heat transfer along the two processes. Then

A
$Q_1 = Q_2$
✓
$Q_1 < Q_2$
C
$Q_1 > Q_2$
D
insufficient data

✓

Answer

Correct option: B.

$Q_1 < Q_2$

b
Let the volumes and temperatures of gas at points 1,2 and 3 are $V_1, T_1, V_2, T_2$ and $V _3, T _3$ respectively.

Given: $T_2=T_3$

Thus $\Delta U _1= nC _{ v }\left( T _2- T _1\right)$

Also $\Delta U _2= nC _{ v }\left( T _3- T _1\right)$

But $T _2= T _3 \Rightarrow \Delta U _1=\Delta U _2$

Work done by the gas in process 1, $W _1= nRT \ln \frac{ V _2}{ V _1}$

Also work done by gas in process $2, \quad W_2=n R T \ln \frac{V_3}{V_1}$

$V _3 > V _2 \Rightarrow W _2 > W _1$

From ist law: $\quad Q=\Delta U+W$

$\therefore \quad Q _{ I }=\Delta U _1+ W _1$

Also $\quad Q _2=\Delta U _2+ W _2$

$\therefore Q _2- Q _1= W _2- W _1>0 \quad\left(\because \Delta U _1=\Delta U _2\right)$

$\Rightarrow Q _2 > Q _1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

NEET STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Assertion : If the temperature of a semiconductor is increased then it’s resistance decreases.
Reason : The energy gap between conduction band and valence band is very small

A piece of wire of resistance $4\, ohms$ is bent through $180^o$ at its mid point and the two halves are twisted together, then the resistance is ............ $ohms$

A ($100\, W$, $200\, V$) bulb is connected to a $160\, V$ power supply. The power consumption would be ............. $W$

At the top of the trajectory of a projectile, the acceleration is

When the pressure on $1200\, ml$ of a gas in increased from $70\, cm $ to $120\, cm$ of mercury at constant temperature, the new volume of the gas will be ........ $ml$

The resistance of the filament of a lamp increases with the increase in temperature. A lamp rated $100\, W, 220\, V$ is connected across $220\, V$ power supply. If the voltage drops by $10\%$ then the power of lamp will be

In a potentiometer circuit a cell of $EMF$ $1.5\, {V}$ gives balance point at $36\, {cm}$ length of wire. If another cell of $EMF$ $2.5\, {V}$ replaces the first cell, then at what length of the wire, the balance point occurs ? (in $cm$)

The given graph shows the variation of velocity with displacement. Which one of the graph given below correctly represents the variation of acceleration with displacement

A particle moves in the $x-y$ plane under the action of a force $\,\vec F$ such that the value of its linear momentum $(\,\vec P)$ at anytime $t$ is $P_x = 2cost$ , $P_y = 2sint$ . The angle between $\,\vec F$ and $\,\vec P$ at a given time $t$ , will be

A man of height $170\,cm$ wants to see his complete image in a plane mirror (while standing). This eyes are at a height of $160 \,cm$ from the ground.

$(a)$ Minimum length of mirror is $80\,cm$

$(b)$ Minimum length of mirror is $85\,cm$.

$(c)$ Bottom of the mirror should be at a height $80\,cm$

$(d)$ Bottom of the mirror should be at a height $85\,cm.$