Advertisements
Advertisements
प्रश्न
An ideal gas expands from 100 cm3 to 200 cm3 at a constant pressure of 2.0 × 105 Pa when 50 J of heat is supplied to it. Calculate (a) the change in internal energy of the gas (b) the number of moles in the gas if the initial temperature is 300 K (c) the molar heat capacity Cp at constant pressure and (d) the molar heat capacity Cv at constant volume.
उत्तर
Initial volume of the gas, V1 = 100 cm3
Final volume = V2 = 200 cm3
Pressure = 2 × 105 Pa
Heat supplied, dQ = 50 J
(a) According to the first law of thermodynamics,
dQ = dU + dW
dW = PΔV = 2 × 105 × (200 -100) × 10-6 = 20
Initial volume of the gas, V1 = 100 cm3
Final volume = V2 = 200 cm3
Pressure = 2 × 105 Pa
Heat supplied, dQ = 50 J
(a) According to the first law of thermodynamics,
dQ = dU + dW
`"U" = 3/2 "n""R""T"`
`30 = n xx 3/2 xx 8.3 xx 300`
`=> n = 2/(83 xx3) = 2/249 = 0.008`(c) Also,
dU = nCvdT
`=> "C"_"V" = ("d""U")/ ("n""d""T") = 30 /(0.008 xx 300) = 12.5`
Cp = Cv + R = 12.5 + 8.3 = 20.8 J/mol-K
(d) Cv = 12.5 J/mol-K
APPEARS IN
संबंधित प्रश्न
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?
Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms:
| Substance | Atomic Mass (u) | Density (103 Kg m-3) |
| Carbon (diamond) | 12.01 | 2.22 |
| Gold | 197.00 | 19.32 |
| Nitrogen (liquid) | 14.01 | 1.00 |
| Lithium | 6.94 | 0.53 |
| Fluorine (liquid) | 19.00 | 1.14 |
[Hint: Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use the known value of Avogadro’s number. You should, however, not take the actual numbers you obtain for various atomic sizes too literally. Because of the crudeness of the tight packing approximation, the results only indicate that atomic sizes are in the range of a few Å].
Does a gas have just two specific heat capacities or more than two? Is the number of specific heat capacities of a gas countable?
Can we define specific heat capacity for an adiabatic process?
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.
In an isothermal process on an ideal gas, the pressure increases by 0.5%. The volume decreases by about
Consider the processes A and B shown in the figure. It is possible that
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.
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.
In Joly's differential steam calorimeter, 3 g of an ideal gas is contained in a rigid closed sphere at 20°C. The sphere is heated by steam at 100°C and it is found that an extra 0.095 g of steam has condensed into water as the temperature of the gas becomes constant. Calculate the specific heat capacity of the gas in J g−1 K−1. The latent heat of vaporisation of water = 540 cal g−1
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.
4.0 g of helium occupies 22400 cm3 at STP. The specific heat capacity of helium at constant pressure is 5.0 cal K−1 mol−1. Calculate the speed of sound in helium at STP.
Molar specific heat of water is C = 74.7 J/mol K, its value in cal/g K is ______.
A diatomic molecule can be modelled as two rigid balls connected with spring such that the balls can vibrate with respect to centre of mass of the system (spring + balls). Consider a diatomic gas made of such diatomic molecule. If the gas performs 20 Joule of work under isobaric condition, then heat given to the gas is ______ J.
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 ______.
