Physics Thermodynamics

The volume V of a given mass of monoatomic gas changes with temperature T according to the relation $V = k T^{\frac{2}{3}} .$ The work done when temperature changes by 90 K will be xR. The value of x is…….

[R = universal gas constant]

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Contributor-Level 10

$V = k T^{\frac{2}{3}}$

-> $T V^{- \frac{3}{2}} = K$

$\Rightarrow γ - 1 = - 3 / 2$

$\Rightarrow γ = - 1 / 2$

Work done = $\frac{n R Δ T}{- y + 1} = \frac{1 * R * 90}{3 / 2} = 6 R$

->n = 60

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2 weeks ago

The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4. The gas is:

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Contributor-Level 10

U = 3PV + 4

^{$\Rightarrow n C_{v} T = 3 P V + 4$}

$\Rightarrow n * \frac{f R T}{2} = 3 P V + 4$

$\Rightarrow f = 6 + \frac{8}{P V}$

$\Rightarrow f > 6 \Rightarrow p o l y a t o m i c$

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2 weeks ago

A diatomic gas, having C_P $= \frac{7}{2} R a n d C_{V} = \frac{5}{2} R,$ is heated at constant pressure. The ratio dU : dQ : dW :

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Vishal Baghel

Contributor-Level 10

At constant pressure,

$d U = n C_{V} d T = n . \frac{5}{2} R d T$

$d Q = n C_{P} d T = n . \frac{7}{2} R d T$

dW = nRdT

dU : dQ : dW = 5 : 7 : 2

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2 weeks ago

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed $υ$ and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by:

(R = universal gas constant)

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Contributor-Level 9

$K E = Δ U$

$Δ U = \frac{1}{2} m v^{2}$

$n C_{v} Δ T = \frac{m v^{2}}{2}$

$\Rightarrow \frac{m}{M} \frac{R}{y - 1} Δ T = \frac{m v^{2}}{2}$

$Δ T = \frac{0.4}{2} \frac{M v^{2}}{R}$

$Δ T = \frac{M v^{2}}{5 R}$

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2 weeks ago

The efficiency of a Carnot's engine, working between stem point and ice point, will be:

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Contributor-Level 9

Steam point (T₁) = 100°C = 273 + 100 = 373 K

Ice point (T₂) = 0°C = 273 K

$η = (1 - \frac{T_{2}}{T_{1}}) * 100 = (1 - \frac{273}{373}) * 100 = 26.81 %$

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2 weeks ago

The total internal energy of two mole mono atomic ideal gas at temperature T = 300K will be __________J. (Given R = 8.31 J/mol.K)

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Contributor-Level 9

$U = n c_{v} T$

$\begin{array}{l} = 2 * \frac{3}{2} * R * 300 \\ = 7479 J \end{array}$

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2 weeks ago

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:

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Contributor-Level 9

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.

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2 weeks ago

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

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Contributor-Level 10

Process-AB $\Rightarrow$ Isobaric,

Process-AC $\Rightarrow$ Isothermal, and

Process-ADÞAdiabatic

W₂ < W₁ < W₃

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3 weeks ago

In an experiment to verigy Newton's law of cooling, a graph is plotted between, the temperature difference $(Δ T)$ of the water and surrounding and time as shown in figure. The initial temperature of water is taken as $80 ° C .$ The value of t₂ as mentioned in the graph will be _______.

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Contributor-Level 10

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

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

$\Rightarrow k = - \frac{1}{6} l n (\frac{2}{3})$ - (1)

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

t = 10.257

t₂ = 6 + 10.257 = 16.257 minutes

16.25 and or 16

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3 weeks ago

An ideal gas undergoes a thermodynamic process in which internal energy $(U)$ of the gas depends on pressure $(P)$ of the gas as $= a P^{4}$ , where a is a positive constant. Assuming gas to be monoatomic, the molar heat capacity of the gas for given process will be

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