Question

5.6dm3 of an unknown gas at Stp requires 52.25J of heat to raise its temperature by 10°c at constant volume. Calculate cv, cp and atomicity of the gas.

Answer 1

HELLO FRIEND HERE IS YOUR ANSWER,,,,,,,,,

At STP a gas of $22.4 \: dm^3$ will be equivalent to " 1 mole".

Therefore for $5.6 \: dm^3$ of the gas at STP will be equivalent to :

= > $\bf{\frac{1}{22.4} \times 5.6}$

= > $\bf{0.25 \: moles}$

As mentioned in the query there is a temperature rise of "10°C", for the value of "0?25 moles" of the gas at a constant volume of 10°C the required heat would be (given) = 52.25 Joules.

Therefore for a rise of temperature in about "1°C", 1 mole of that gas in a constant volume will've the heat requirement of :

= > $\bf{\frac{52.25}{10 \times 0.25} \: Joules}$

= >$\bf{\frac{52.25}{2.5} \: Joules}$

= > $\bf{20.9 \: Joules}$

$\boxed{\bf{\therefore \: \: C_v = 20.9 \: Joule \: Kelvin^{- 1} \: mole^{- 1}}}$

Therefore, to calculate $\bf{C_p}$.

$\bf{C_p = C_v + R}$

$\bf{\therefore \: \: C_p = 20.9 \: Joule \: Kelvin^{- 1} \: Mole^{- 1} + 8.314 \: Joule \: Kelvin^{- 1} \: Mole^{- 1}}$

$\boxed{\bf{\therefore \: \: C_p = 29.214 \: Joule \: Kelvin^{- 1} \: Mole^{- 1}}}$

Now, for calculating the unknown gas's atomicity or to check whether it's monoatomic, diatomic etc.

$\bf{\therefore \: \: \gamma = \frac{C_p}{C_v}}$

$\bf{\therefore \: \: \gamma = \frac{29.214}{20.9}}$

$\boxed{\bf{\therefore \: \: \gamma = 1.4}}$

Therefore the given unknown gas's atomicity is $\boxed{\bf{Diatomic \: Gas}}$.

HOPE THIS HELPS YOU AND SOLVES YOUR DOUBTS FOR THIS QUERY !!!!!

Answer 2

At STP a gas of will be equivalent to " 1 mole".

Therefore for of the gas at STP will be equivalent to :

= >

= >

As mentioned in the query there is a temperature rise of "10°C", for the value of "0?25 moles" of the gas at a constant volume of 10°C the required heat would be (given) = 52.25 Joules.

Therefore for a rise of temperature in about "1°C", 1 mole of that gas in a constant volume will've the heat requirement of :

= >

= >

= >

Therefore, to calculate .

Now, for calculating the unknown gas's atomicity or to check whether it's monoatomic, diatomic etc.

Therefore the given unknown gas's atomicity is .

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