Given below are two statements: Statement – I : When μ moment of an ideal gas undergoes adiabatic change from state ( P 1 , V 1 , T 1 ) to state ( P 2 , V 2 , T 2 ) then work done is w = μ R ( T 2 − T 1 ) 1 − γ , where γ = C p C v a n d R = universal gas constant. Statement – II : In the above case, when work done on the gas, the temperature of the gas would rise. Choose the correct answer from the options given below:

In case of adiabatic process Work done, W=ηR (T2−T1)1−Y As, ΔQ=ΔU+W for adiabatic process :- ΔQ=0 ⇒ΔU=−W So, when work is done by the gas, temperature decreases and when work is done on the gas, temperature rises.

Given below are two statements:

Statement – I : When $μ$ moment of an ideal gas undergoes adiabatic change from state $(P_{1}, V_{1}, T_{1})$ to state $(P_{2}, V_{2}, T_{2})$ then work done is w = $\frac{μ R (T_{2} - T_{1})}{1 - γ},$ where $γ = \frac{C_{p}}{C_{v}} a n d$ R = universal gas constant.

Statement – II : In the above case, when work done on the gas, the temperature of the gas would rise.

Choose the correct answer from the options given below:

Option 1 - Both statement – I and statement – II are true.

Option 2 - Both statement – I and statement – II are false.

Option 3 - Statement – I is true but statement – II is false.

Option 4 - Statement – I is false but statement – II is true.

2 Views|Posted 7 months ago

Asked by Shiksha User

1 Answer

Sort by:

Answered by

Payal Gupta | Contributor-Level 10

7 months ago

Correct Option - 1

Detailed Solution:

In case of adiabatic process

$W o r k d o n e, W = \frac{η R (T_{2} - T_{1})}{1 - Y}$

$A s, Δ Q = Δ U + W$

for adiabatic process :- $Δ Q = 0$

$\Rightarrow Δ U = - W$

So, when work is done by the gas, temperature decreases and when work is done on the gas, temperature rises.

Upvote

Similar Questions for you

Starting with the same initial conditions, an ideal gas expands form volume V₁ to V₂ in the three different ways. The work done by the gas in W₁ if the process is purely isothermal, W₂, if the process is purely adiabatic and W₃ if the process is purely isobaric. Then, choose the correct option

Vishal Baghel

Process-AB $\Rightarrow$ Isobaric, &n

Vishal Baghel

from newtan’s law of cooling :

$\frac{d T}{d t} = - k (T - T_{0})$

Using average value :

$\frac{75 - 65}{5} = - k [\frac{(75 + 65) 2}{2} - 25]$

$\frac{(65 - T)}{5} = - k [\frac{(65 + T)}{2} - 25]$

$\Rightarrow \frac{10}{65 - T} = \frac{45}{\frac{65 + T}{2} - 25}$

$\Rightarrow T = 57 ° C$

A Carnot engine has efficiency of 50%. If the temperature of sink is reduced by 40°C, its efficiency increases by 30%. The temperature of the source will be:

Vishal Baghel

Efficiency $η = 50 %$

$\Rightarrow η = (1 - \frac{T_{2}}{T_{1}}) \times 100 = 50$

$\Rightarrow 1 - \frac{T_{2}}{T_{1}} = \frac{50}{100} \Rightarrow 1 - \frac{T_{2}}{T_{1}} = \frac{1}{2}$ -(i)

After the change :- $1 - \frac{T_{2}^{1}}{T_{1}} = \frac{50 \times (1.3)}{100} = \frac{65}{100} = . 65$ $\frac{_{}^{}}{_{}} \frac{}{} \frac{}{}$ -(ii)