CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Thermodynamic Processes

One mole of a...

Question

One mole of an ideal monoatomic gas has initial temperature $T_{0}$ is made to go through the cyclic process $a b c a$ as shown in figure. If $U$ denotes the internal energy, then choose the correct alternative.

A

U_{c} > U_{b} > U_{a}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

U_{c} - U_{b} = 3 R T_{0}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

C

U_{c} - U_{A} = \frac{9 R T_{0}}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

U_{b} - U_{a} = \frac{3 R T_{0}}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct options are
A $U_{c} > U_{b} > U_{a}$
B $U_{c} - U_{b} = 3 R T_{0}$
C $U_{c} - U_{A} = \frac{9 R T_{0}}{2}$
D $U_{b} - U_{a} = \frac{3 R T_{0}}{2}$

For process $a b$ [isobaric]
$\frac{V_{a}}{T_{a}} = \frac{V_{b}}{T_{b}} \Rightarrow \frac{V_{0}}{T_{0}} = \frac{2 V_{0}}{T_{b}}$
$T_{b} = 2 T_{0} \Rightarrow T_{b} > T_{a} \Rightarrow U_{b} > U_{a}$
$U_{b} - U_{a} = C_{V} Δ T = \frac{3 R}{2} (2 T_{0} - T_{0}) = \frac{3 R T_{0}}{2}$
For process $b c$ (isochoric process)
$\frac{P_{b}}{T_{b}} = \frac{P_{c}}{T_{c}} \Rightarrow \frac{P_{0}}{2 T_{0}} = \frac{2 P_{0}}{T_{c}} \Rightarrow T_{c} = 4 T_{0}$
$\Rightarrow T_{c} > T_{a} \Rightarrow U_{c} > U_{a}$
$U_{c} - U_{b} = \frac{3 R}{2} (4 T_{0} - 2 T_{0}) = 3 R T_{0} \Rightarrow U_{c} > U_{b}$
For process $c a$ :
$U_{c} - U_{a} = \frac{3 R}{2} (4 T_{0} - T_{0}) = \frac{9 R T_{0}}{2}$
Thus, we can conclude that,
Options (a), (b), (c) and (d) are the correct answers.

Suggest Corrections

thumbs-up

0

Similar questions

Q. One mole of an ideal monatomic gas has initial temperature

T_{0}

, is made to go through the cycle

a b c a

as shown in fig. If

U

denotes the internal energy, then choose the correct alternative.

Q. One mole of an ideal monatomic gas has initial temperature

T_{0}

is made to go through the cycle

a b c a

as shown in the given figure. If

U

denotes the internal energy, then choose the correct alternative.

Q. One mole of an ideal monoatomic gas has initial temperature

T_{0}

is made to go through the cyclic process

a b c a

as shown in figure. If

U

denotes the internal energy, then choose the correct alternative.

Q. One mole of an ideal monatomic gas has initial temperature

T_{0}

is made to go through the cycle

a b c a

as shown in the given figure. If

U

denotes the internal energy, then choose the correct alternative.

Q. An ideal monoatomic gas is taken through the theromodynamic states

A \to B \to C \to D

via the paths shown in the figure. If

U_{A}, U_{B}, U_{C}

U_{D}

represent the internal energy of the gas in states A, B, C and D respectively, then which of the following is not true?

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Thermodynamic Processes

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon