Advertisements
Advertisements
Question
A mixture contains 1 mole of helium (Cp = 2.5 R, Cv = 1.5 R) and 1 mole of hydrogen (Cp= 3.5 R, Cv = 2.5 R). Calculate the values of Cp, Cv and γ for the mixture.
Advertisements
Solution
Specific heat at constant pressure of helium, Cp' = 2.5 R
Specific heat at constant pressure of hydrogen, Cp" = 3.5 R
Specific heat at constant volume of helium, Cv' = 1.5 R
Specific heat at constant volume of hydrogen, Cv" = 2.5 R
n1 = n2 = 1 mol
dU = nCvdT
For the mixture of two gases,
dU1 +dU2 = 1 mol
[n1 + n2] CvdT = n1C'vdT + n2C"vdT,
where Cv is the heat capacity of the mixture
`=> "C"_"v" =("n"_1"C"'_"v" + "n"_2"C"''_"v")/("n"_1+"n"_2)`
`= (1.5"R" +2.5"R")/2 =2"R"`
Cp = Cv + R = 2R + R = 3R
`gamma = "C"_"p"/"C"_"v" = (3"R")/(2"R") = 1.5`
APPEARS IN
RELATED QUESTIONS
A metre long narrow bore held horizontally (and closed at one end) contains a 76 cm long mercury thread, which traps a 15 cm column of air. What happens if the tube is held vertically with the open end at the bottom?
The specific heat capacity of water is
Does a gas have just two specific heat capacities or more than two? Is the number of specific heat capacities of a gas countable?
Does a solid also have two kinds of molar heat capacities Cp and Cv? If yes, is Cp > Cv? Or is Cp − Cv = R?
In a real gas, the internal energy depends on temperature and also on volume. The energy increases when the gas expands isothermally. Examining the derivation of Cp − Cv = R, find whether Cp − Cv will be more than R, less than R or equal to R for a real gas.
Can a process on an ideal gas be both adiabatic and isothermal?
Show that the slope of the p−V diagram is greater for an adiabatic process compared to an isothermal process.
Two samples A and B are initially kept in the same state. Sample A is expanded through an adiabatic process and the sample B through an isothermal process. The final volumes of the samples are the same. The final pressures in A and B are pA and pBrespectively.
Let ∆Wa and ∆Wb be the work done by the systems A and B, respectively, in the previous question.
5 g of a gas is contained in a rigid container and is heated from 15°C to 25°C. Specific heat capacity of the gas at constant volume is 0.172 cal g−1 °C−1 and the mechanical equivalent of heat is 4.2 J cal−1. Calculate the change in the internal energy of the gas
A sample of air weighing 1.18 g occupies 1.0 × 103 cm3 when kept at 300 K and 1.0 × 105 Pa. When 2.0 cal of heat is added to it at constant volume, its temperature increases by 1°C. Calculate the amount of heat needed to increase the temperature of air by 1°C at constant pressure if the mechanical equivalent of heat is 4.2 × 107 erg cal−1. Assume that air behaves as an ideal gas.
The figure shows two vessels with adiabatic walls, one containing 0.1 g of helium (γ = 1.67, M = 4 g mol−1) and the other containing some amount of hydrogen (γ = 1.4, M = 2 g mol−1). Initially, the temperatures 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 the temperatures rise through the same amount in the two vessels. Calculate the mass of hydrogen.
The speed of sound in hydrogen at 0°C is 1280 m s−1. The density of hydrogen at STP is 0.089 kg m−3. Calculate the molar heat capacities Cp and Cv of hydrogen.
Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities Cp and Cv of the gas.
Molar specific heat of water is C = 74.7 J/mol K, its value in cal/g K is ______.
An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to `1/10^"th"` of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ______.
If at same temperature and pressure, the densities for two diatomic gases are respectively d1 and d2 then the ratio of velocities of sound in these gases will be ______.
