Question

1. Under constant-volume conditions, 4200 J of heat is added to 1.4 moles of an ideal gas. As a result, the temperature of the gas increases by 103 K. How much heat would be required to cause the same temperature change under constant-pressure conditions? Do not assume anything about whether the gas is monatomic, diatomic, etc.

2. A system gains 3080 J of heat at a constant pressure of 1.36 × 105 Pa, and its internal energy increases by 4160 J. What is the change in the volume of the system, and is it an increase or a decrease? ΔV = Entry field with correct answer Entry field with incorrect answer Entry field with correct answer

3. A system undergoes a two-step process. In the first step, the internal energy of the system increases by 229 J when 166 J of work is done on the system. In the second step, the internal energy of the system increases by 115 J when 193 J of work is done on the system. For the overall process, find the heat added to the system (including sign).

Answer #1

**Solution (1):**

At constant volume, heat added in a gas is given by

(1)

At constant pressure, heat added in a gas is given by

(2)

Given that:

Putting the value of from equation (1), in (2), we find

(3)

So, for same increase in temperature, the heat added in constant Pressure Process is times of head added in constant volume Process.

In a constant-volume process, 208 J of energy is transferred by
heat to 1.08 mol of an ideal monatomic gas initially at 294 K.
(a) Find the work done on the gas.
J
(b) Find the increase in internal energy of the gas.
J
(c) Find its final temperature.
K

In a constant-volume process, 215 J of energy
is transferred by heat to 1.07 mol of an ideal
monatomic gas initially at 292 K.
(a) Find the work done on the gas.
0 J
(b) Find the increase in internal energy of the gas.
215 J
(c) Find its final temperature.
? K

Three moles of a monatomic ideal gas are heated at a constant
volume of 2.90 m3. The amount of heat added is 5.10 103 J.
(a) What is the change in the temperature of the gas?
_____K
(b) Find the change in its internal energy.
_____J
(c) Determine the change in pressure.
_____Pa

When 18.5 J was added as heat to a particular ideal gas, the
volume of the gas changed from 36.8 cm3 to 59.4
cm3 while the pressure remained constant at 0.944 atm.
(a) By how much did the internal energy of the gas
change? If the quantity of gas present is 1.38 x 10-3
mol, find the molar specific heat of the gas at
(b) constant pressure and (c)
constant volume.

2.)1.0 mol sample of an ideal monatomic gas originally at a
pressure of 1 atm undergoes a 3-step process as follows:
(i) It expands
adiabatically from T1 = 588 K to T2 = 389 K
(ii) It is compressed at
constant pressure until its temperature reaches T3 K
(iii) It then returns to its
original pressure and temperature by a constant volume process.
A). Plot these processes on a PV diagram
B). Determine the temperature T3
C)....

Under constant pressure, the temperature of 1.70 mol of an ideal
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In this problem, 0.90 mole of a monatomic ideal gas is initially
at 285 K and 1 atm.
(a) What is its initial internal energy?
_____ kJ
(b) Find its final internal energy and the work done by the gas
when 420 J of heat are added at constant pressure.
final internal energy ________kJ
work done by the gas _______kJ
(c) Find the same quantities when 420 J of heat are added at
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finale internal energy ________kJ
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(a) Use the ideal gas law and initial conditions to calculate
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The heat capacity at constant volume of a certain amount of a
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(a) Find the number of moles of the gas. in mol
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Consider the following four-process cycle that is carried out on
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Process A is an isothermal process that triples the
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process B is a constant volume process that returns the system to a
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process C is an isothermal process that returns the system to a
volume of 3.00 liters;
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