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In the given graph an ideal gas changes its state from A to st

Question

In the given graph an ideal gas changes its state from $A$ to state $C$ by two paths $A BC$ and $A C$ . The internal energy of gas at $A$ is $10 J$ and the amount of heat supplied in path $A C$ is $200 J$ . The internal energy $(in J)$ of gas at $C$ is $6 k^{2}$ . What is the value of $k$ ?

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In the given graph an ideal gas changes its state from

A

to state

C

by two paths

A BC

and

A C

. The internal energy of gas at

A

10 J

and the amount of heat supplied in path

A C

200 J

. The internal energy

(in J)

of gas at

C

6 k^{2}

. What is the value of

k

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Text solutionVerified

The first law of thermodynamics states that:

δ Q = Δ U + w = Δ U + \int P d V

Work done =

\int P d V

= area under graph between A and C

Area under graph

= 60 J

Given that

δ Q = 200 J

i.e.

Δ U = 140 J

Δ U = U_{2} - U_{1} = 140 J = U_{2} - 10 J

i.e.

U_{2} = 150 J

\Rightarrow 6 k^{2} = 150

\Rightarrow k = 5

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Question Text	In the given graph an ideal gas changes its state from $A$ to state $C$ by two paths $A BC$ and $A C$ . The internal energy of gas at $A$ is $10 J$ and the amount of heat supplied in path $A C$ is $200 J$ . The internal energy $(in J)$ of gas at $C$ is $6 k^{2}$ . What is the value of $k$ ?
Answer Type	Text solution:1
Upvotes	150