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Physics-

General

Easy

Question

The temperature of equal masses of three different liquids A, B and C are $12 to the power of ring operator end exponent C comma 19 to the power of ring operator end exponent c$ and $28 to the power of ring operator end exponent C$ respectively. The temperature when A and B are mixed is $16 to the power of ring operator end exponent C$ and when $B$ and $C$ are mixed it is $23 to the power of ring operator end exponent C$ . What should be the temperature when A and C are mixed ?

${20.26}^{\circ} C$
${15.87}^{\circ} C$
$25^{\circ} C$
$30^{\circ} C$

The correct answer is: $20.26 to the power of ring operator end exponent C$

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Compressibility factor (Z): Real gases deviate from ideal behavior due to the following two faulty assumptions of kinetic theory of gases.
i)Actual volume occupied by the gas molecule is negligible as compared to the total volume of the gases.
ii)Forces of attraction and repulsion among the gas molecules are negligible.
the, extent of deviation of the real gas from ideal behaviour, is explained in terms of compressibility factor (Z), which is function of pressure and temperature for real gas.
For ideal gas, Z = 1
For real gases, Z > 1 or Z < 1
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On increasing temperature, Z increases and approaches to unity. Graph between
Z and P at different temperature for the same gas is shown as under:

The van der Waal’s equation of state for 1 mole of gas is as under:
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Where a and b are van der Waal’s constants.
van der Waal’s constant “a” measures the amount of the force of attraction among the gas molecules. Higher the value of “a”, higher will be the ease of liquefaction.
Case (1)For H₂ and He then equation into –I will reduce P(V – b) = RTCase (2) When pressure is too low i.e. for N₂ or CH₄ or, CO₂ then equation (–I) reduces into $open parentheses P plus fraction numerator a over denominator V to the power of 2 end exponent end fraction close parentheses V equals R T$
Which of the following statement is correct as shown in the above graph?

Compressibility factor (Z): Real gases deviate from ideal behavior due to the following two faulty assumptions of kinetic theory of gases.
i)Actual volume occupied by the gas molecule is negligible as compared to the total volume of the gases.
ii)Forces of attraction and repulsion among the gas molecules are negligible.
the, extent of deviation of the real gas from ideal behaviour, is explained in terms of compressibility factor (Z), which is function of pressure and temperature for real gas.
For ideal gas, Z = 1
For real gases, Z > 1 or Z < 1
When Z > 1, then it is less compressible because force of repulsion dominates over force of attraction when Z < 1, force of attraction dominates over the force repulsion.
Graph in between Z & P is shown as under

On increasing temperature, Z increases and approaches to unity. Graph between
Z and P at different temperature for the same gas is shown as under:

The van der Waal’s equation of state for 1 mole of gas is as under:
$open parentheses P plus fraction numerator a over denominator V to the power of 2 end exponent end fraction close parentheses left parenthesis V minus b right parenthesis equals R T$ …(1)
Where a and b are van der Waal’s constants.
van der Waal’s constant “a” measures the amount of the force of attraction among the gas molecules. Higher the value of “a”, higher will be the ease of liquefaction.
Case (1)For H₂ and He then equation into –I will reduce P(V – b) = RTCase (2) When pressure is too low i.e. for N₂ or CH₄ or, CO₂ then equation (–I) reduces into $open parentheses P plus fraction numerator a over denominator V to the power of 2 end exponent end fraction close parentheses V equals R T$
Which of the following statement is correct as shown in the above graph?

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