Question

The temperature of 5 moles of a gas which was held at constant volume was changed from 100 degree celsius to 120 degree celsius. The change in internal energy was found to be 80 joules. The total heat capacity of the gas at constant volume will be equal to a. 8 J/K b. 0.8 J/K c. 4.0 J/K d. 0.4 J/K

Answer 1

Given :

▪ Moles of gas = 5

▪ Initial temp. = 100°C

▪ Final temp. = 120°C

▪ Change in internal energy = 80J

To Find :

➳ Heat capacity of gas at constant volume.

SoluTion :

⇒ Heat loss or gained by a gas (change in internal energy) at constant volume is given by

$\bigstar\:\boxed{\bf{Q=nC_v\Delta T}}$

• n denotes mole
• Cv denotes heat capacity
• ΔT denotes change in temp.

$\leadsto\sf\:Q =mC_v\Delta T$

$\leadsto\sf\:80=5\times C_v\times (120-100)$

$\leadsto\sf\:80=100\times C_v$

$\leadsto\boxed{\bf{\purple{C_v=0.8\:JK^{-1}}}}$

Answer 2

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Answer:-

Given,

• Moles of a gas = 5
• Initial temperature = 100°c
• Final temperature = 120°c
• Change in internal energy = 80j

To Find:-

✔✔Heat capacity of a has at constant volume✔✔

Calculations:-

Q =nCv∆T

Now substituting the given values:-

80=5×Cv×(120-100)

80=100 × Cv

$c_{v} = 0.8 {jk}^{ - 1}$

Heat capacity of a gas at constant volume is 0.8jk^-1

$\sf{\underline{\underline{More:}}}$

Internal energy:-

• Internal energy of a system is the sum of potential energy and kinetic energy of the system.

∆u = q + w

• The internal energy is additionally associated with potential energies.

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