Advertisements
Advertisements
Question
Can we define specific heat capacity for an adiabatic process?
Advertisements
Solution
Specific heat capacity, s =`(triangle "Q")/(m triangleT)`, where `(triangle "Q")/m` is the heat supplied per unit mass of the substance and ΔT is the change in temperature produced. In an adiabatic process, no heat exchange is allowed; so, ΔQ = 0 and hence, s = 0. Therefore, in an adiabatic process, specific heat capacity is zero.
APPEARS IN
RELATED QUESTIONS
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?
Does a solid also have two kinds of molar heat capacities Cp and Cv? If yes, is Cp > Cv? Or is Cp − Cv = R?
Can a process on an ideal gas be both adiabatic and isothermal?
Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?
In an isothermal process on an ideal gas, the pressure increases by 0.5%. The volume decreases by about
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.
Three identical adiabatic containers A, B and C contain helium, neon and oxygen, respectively, at equal pressure. The gases are pushed to half their original volumes.
(a) The final temperatures in the three containers will be the same.
(b) The final pressures in the three containers will be the same.
(c) The pressures of helium and neon will be the same but that of oxygen will be different.
(d) The temperatures of helium and neon will be the same but that of oxygen will be different.
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.
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.
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.
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 ______.
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.
