Advertisements
Advertisements
Question
What amount of heat must be supplied to 2.0 x 10-2 kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure? (Molecular mass of N2 = 28; R = 8.3 J mol-1 K-1.)
Advertisements
Solution 1
Mass of nitrogen, m = 2.0 × 10–2 kg = 20 g
Rise in temperature, ΔT = 45°C
Molecular mass of N2, M = 28
Universal gas constant, R = 8.3 J mol–1 K–1
Number of moles, `n = m/M`
`= (2.0xx10^(-2)xx10^3)/28 = 0.714`
Molar specific heat at constant pressure for nitrogen, `C_P = 7/2 R`
`= 7/2 xx 8.3`
`= 29.05 J mol^(-1) K^(-1)`
The total amount of heat to be supplied is given by the relation:
ΔQ = nCP ΔT
= 0.714 × 29.05 × 45
= 933.38 J
Therefore, the amount of heat to be supplied is 933.38 J.
Solution 2
Here, mass of gas,` m= 2xx 10^-2 kg` = 20 g
rise in temperature, `triangleT = 45 ^@C`
Heat required, triangleQ = ?, Molecular mass, M = 28
Number of moles , `n = m/M = 20/28 = 0.714`
As nitrogen is a diatomatic gas,molar specific heat at constant pressure is
`C_p = 7/2R = 7/2 xx 8.3 J mol^(-1) K^(-1)`
As `triangleQ = nC_p triangleT`
`:. triangleQ = 0.714 xx 7/2 xx 8.3 xx 45 J = 933.4 J`
APPEARS IN
RELATED QUESTIONS
What do you understand by the following statements:
The heat capacity of the body is 60JK-1.
What do you understand by the following statements:
The specific heat capacity of lead is 130 Jkg-1K-1.
Water in lakes and ponds do not freeze at once in cold countries. Give a reason is support of your answer.
A solid metal weighing 150 g melts at its melting point of 800 °C by providing heat at the rate of 100 W. The time taken for it to completely melt at the same temperature is 4 min. What is the specific latent heat of fusion of the metal?
Give one example where high specific heat capacity of water is used as heat reservoir ?
In an experiment to determine the specific heat capacity of a solid following operations were
made:
Mass of calorimeter + stirrer = x kg
Mass of water = y kg
Initial temperature of water t1℃
Mass of solid = z kg
Temperature of solid = t2 ℃
Temperature of mixture = t ℃
Specific heat capacity of calorimeter and water are c1 and c2 respectively. Express the specific
heat capacity c of the solid in terms of the above data.
Find the time taken by a 500 W heater to raise the temperature of 50 kg of material of specific heat capacity 960 J kg-1K-1, from 18°C to 38° C. Assume that all the heat energy supplied by the heater is given to the material.
Name two green house gases ?
State the impact of global warming on life on the earth.
Name and state the principle used to measure the specific heat capacity of a substance.
Figure shows a paddle wheel coupled to a mass of 12 kg through fixed frictionless pulleys. The paddle is immersed in a liquid of heat capacity 4200 J K−1 kept in an adiabatic container. Consider a time interval in which the 12 kg block falls slowly through 70 cm. (a) How much heat is given to the liquid? (b) How much work is done on the liquid? (c) Calculate the rise in the temperature of the liquid neglecting the heat capacity of the container and the paddle.
A substance is heated at a constant rate from a low temperature to a high temperature. A graph of temperature against time is shown in the figure. Which part or parts of the graph correspond(s) to the substance existing in two states?
What change in heat energy occurs when lead at its melting point
solidifies without change in the temperature?
Name the substance which has maximum specific heat capacity.
Does the specific heat capacity of a substance depend upon its mass and rise in temperature only?
Why is specific heat capacity taken as a measure of thermal inertia?
Specific heat capacity of substance A is 3.8 J g-1 K-1whereas the specific heat capacity of substance B is 0.4 J g-1 K-1. Which of the two is a good conductor of heat? How is one led to this conclusion?
Give two reasons as to why copper is preferred over other metals for making calorimeters.
Ice-cream at 0°C feels colder than water at 0°C. Give reason for this observation.
1 kg of water freezes to form ice at 0°C. What amount of heat is withdrawn?
A substance is in the form of a solid at 0°C. The amount of heat added to this substance and the temperature of the substance are plotted on the following graph:
If the specific heat capacity of the solid substance is 500 J/kg °G, find from the graph, the mass of the substance.
Solve the following problem.
What is the specific heat of metal if 50 cal of heat is needed to raise 6 kg of the metal from 20°C to 62 °C?
Explain how heat capacity of a solid can be determined by the method of mixture.
The cold object the hot object enclosed in one box of heat-resistant material.
- What changes will occur in the two objects when temperature flows from those objects?
- Which principle can show that the energy exchange takes place between two objects only when kept in isolated system?
Numerical Problem.
What is the heat in joules required to raise the temperature of 25 grams of water from 0°C to 100°C? What is the heat in Calories? (Specific heat of water = `(4.18"J")/("g"°"C")`
Numerical Problem.
What could be the final temperature of a mixture of 100 g of water at 90 °C and 600g of water at 20°C.
50 g of copper is heated to increase its temperature by 10° C. If the same quantity of heat is given to 5 g water, the rise in its temperature is [Specific heat of copper = 420 joule-kg-1 °C-1 , specific heat of water = 4200 joule-kg-I °C-1]
Which of the substances P, Q, or R has the lowest specific heat? The temperature v/s time graph is shown ______.
A monoatomic gas of pressure 'P' having volume 'V' expands isothermally to a volume '2V' and then adiabatically to a volume '16V'. The final pressure of the gas is ______.
(ratio of specific heats = `5/3`)
The ratio of the specific heats `c_"p"/c_"v"=gamma` in terms of degrees of freedom 'n' is given by ______.
What is the amount of heat required to raise the temperature of 5 kg of iron from 30°C to 130°C? Specific heat capacity of iron = 483 Jkg-1C-1.
A metal ball of heat capacity 50J/°C loses 2000 J of heat. By how much will its temperature fall?
A geyser heats water flowing at a rate of 2.0 kg per minute from 30°C to 70°C. If the geyser operates on a gas burner, the rate of combustion of fuel will be ______ g min-1.
[Heat of combustion = 8 × 103 Jg-1 Specific heat of water = 4.2 Jg-1°C-1]
When two kilocalories of heat are supplied to a system, the internal energy of the system increases by 5030 J and the work done by the gas against the external pressure is 3350 J. Calculate J, the mechanical equivalent of heat.
Specific heat capacity of a substance X is 1900 Jkg-1°C-1 means ______.
A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature (27°C). The ratio of specific heat of gases at constant volume respectively is:
