A certain substance has a mass per mole of $$50.0\ mol$$. When $$314\ J$$ is added to a $$30.0\ g$$ sample, the sample's temperature rises from $$25.0^oC$$ to $$45.0^oC$$. How many moles are in the sample?
If $$N$$ is the number of moles of the substance and $$M$$ is the mass per mole, then $$m=NM$$, so
$$N=\dfrac{m}{M}=\dfrac{30.0\times 10^{-3}\ kg}{50\times 10^{-3}\ kg/mol}=0.600\ mol$$.
5 g of a gas is contained in a rigid container and is heated from $$ 15^o C to 25^o C $$. Specific heat capacity of the gas at constant volume is 0.172 cal $$ g^{-1}{^{ o}}C^{-1} $$ . and the mechanical equivalent of heat is $$ 4.2 J cal^{-1} $$. Calculate the charge in the intenal energy of the gas.
The ratio of the molar heat capacities of an ideal gas is $$ C_p / C_v = 7.8 $$ . Calculate the change in internal energy of 1.0 mole of the gas when its temperature is raised by 50 K (a) keeping the pressure constant (b) keeping the volume constant and (c) adiabatically.
A mixture contains 1 mole of helium $$ (C_p = 2.5 R C_v = 1.5 R) $$ and 1 mole of hydrogen $$ (C_p = 3.5 R C_v = 2.5 R) $$ Calculate the value of $$ C_p C_v and \gamma $$ for the mixture.
A mixture contains 1 mole of helium $$ (C_p = 2.5 R C_v = 1.5 R) $$ and 1 mole of hydrogen $$ (C_p = 3.5 R C_v = 2.5 R)$$ Calculate the values of $$ C_p, C_v$$ and $$\gamma $$ for the mixture.
Two sample A and B of the same gas have equal volumes and pressure. The gas in sample A is expanded isothermally to double its volume and the gas in B is expanded adiabatically to double its volume.If the work done by the gas is the same for the two cases, show that $$ \gamma $$ satisfies the equation $$ 1-2^{1-\gamma} =(\gamma-1) $$ In2
Shows two vesels with adiabatic.walls one containing 0.1 g of helium $$ (\gamma = 1.67, M = 4 g mol^{-1} ) $$and the other containing some amount of hydrogen $$ (\gamma = 1.4, M = 2 g mol^{-1} ) $$. Initially , the temperature of the two gases are equal. The gases are electrically heated for.some time during which equal amounts of heat are given to the two gases.It is found that thhe temperature rise through the same amount in the two vessel.Calculate the mass of hydrogen.
The molar specific heat of mixture at constant volume, if one mole of a monoatomic gas is mixed with three moles of a diatomic gas is :
Calculate the value of $$\gamma = C_p/C_v$$ for a gaseous mixture consisting of $$v_1 = 2.0$$ moles of oxygen and $$v_2 = 3.0$$ moles of carbon dioxide. The gases are assumed to be ideal.
Three moles of an ideal gas being initially at a temperature $$T_0 = 273 \ K$$ were isothermally expanded $$n = 5.0$$ times its initial volume and then isochorically heated so that the pressure in the final state became equal to that in the initial state. The total amount of heat transferred to the gas during the process equals $$Q = 80 \ kJ$$. Find the ratio $$\gamma = C_p/C_v $$ for this gas.
Find the adiabatic exponent $$\gamma$$ for a mixture consisting of $$v_1$$ moles of a monatomic gas and $$v_2$$ moles of gas of rigid diatomic molecules.