The value of the heat capacity for a substance depends on whether it’s measured under constant pressure conditions or constant volume conditions. The constant-pressure molar heat capacity is given by
= (dq/dT)P
and the constant-volume heat capacity is given by
= (dq/dT)V
Note that we use d instead of
because q is not a state function of temperature, volume, and
pressure; its value depends on how we execute the process.
Here are several questions regarding heat capacity.
a. When we heat a substance, such as a gas, at constant pressure, does its volume increase, decrease, or remain the same? Is w positive, negative, or zero?
b. When we heat a substance, such as a gas, at constant volume, does its volume increase, decrease, or remain the same? Is w positive, negative, or zero?
c. We transfer the same amount of thermal energy into a gas under constant pressure, and constant volume conditions. Which set of conditions results in a greater change in the temperature of the gas?
d. Explain why a-c imply that the constant-pressure heat capacity for any substance is larger than the constant-volume heat capacity.
a. Volume increases. Work done is negative.
b. Volume remains the same. Work done is zero.
c. The change in temperature shall be more for the system with constant volume because the entire heat energy supplied contributes to the change in temperature as the work done is zero.
d. The constant-pressure heat capacity for any substance is larger than the constant-volume heat capacity because of the non-zero work for an isobaric process as compared to the zero work for isochoric process.
The value of the heat capacity for a substance depends on whether it’s measured under constant...
The amount of heat needed to raise the temperature of 1 mole of a substance by one Celsius degree (or, equivalently, one kelvin) is called the molar heat capacity of the system, denoted by the letter C. If a small amount of heat dQ is put into n moles of a substance, and the resulting change in temperature for the system is dT, then C=1ndQdT. This is the definition of molar heat capacity--the amount of heat Q added per infinitesimal...
Ch 19 HW Relationships between Molar Heat Capacities 9 of 23 Constants The amount of heat needed to raise the temperature of 1 mole of a substance by one Celsius degree (or, equivalently, one kelvin) is called the molar heat capacity of the system, denoted by the letter C. If a small amount of heat dQ is put into n moles of a substance, and the resulting change in temperature for the system is dT, then Part A Consider an...
The molar heat capacity of an unknown gas at constant volume depends on its temperature as: Cv,m = 12.8 kJ moll.K1 +0.0091 kJ molK2xT What is the change in internal energy of 1 mol of this gas as its temperature increases from 278 K to 357 K? (The sign matters!)
(b) The constant-pressure heat capacity of a sample of 1 00 mol of a perfect gas was found to vary with temperature according to the expression Cp/(J K)20 17 + 0 4001 (TK) Calculate q, w, AU and AH when the temperature is raised from 0°C to 100°C ) at constant pressure (u) at constant volume (10)
(b) The constant-pressure heat capacity of a sample of 1 00 mol of a perfect gas was found to vary with temperature according...
3,1 moles of an ideal gas with a molar heat capacity at constant volume of 5,1 cal/(mol∙K) and a molar heat capacity at constant pressure of 7,7 cal/(mol∙K) starts at 317,6 K and is heated at constant pressure to 335,9 K, then cooled at constant volume to its original temperature. How much heat (cal) flows into the gas during this two-step process? Answer in two decimal places.
The equilibrium constant for the following reaction
can be expressed by the empirical formula
in the interval 445 K < T < 460 K. Use this expression to
calculate ∆rH◦ and ∆rS ◦ at 450 K and derive
an equation for ∆fH◦ of Ag2O (s) in this
temperature range. Now use the following heat capacity data:
to calculate ∆rH◦ , ∆rS◦ , and
∆rG◦ at 298 K. Would Ag2O be automatically
decomposed when exposed to the atmosphere (the partial pressure...
Consider a paramagnetic material that obeys Curie's
Law,
where Cc is a constant, and whose heat capacity at
constant magnetization is
with constant A also
Assume that a Carnot cycle is performed using
paramagnetic solids as working material (i.e. as the ideal gas in
the usual case). Show that
with obvious notation
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Under constant-volume conditions the heat of combustion of benzoic acid (C6H5COOH) is 26.38 kJ/g. A 2.790 −g sample of benzoic acid is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.60 ∘C to 29.95 ∘C. A. What is the total heat capacity of the calorimeter? B. A 1.460 −g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 22.14 ∘C to 27.09 ∘C. What is the...
Calculating specific heat capacity A constant-pressure calorimeter is often used to find the specific heat capacity of a substance if it is not known. A known mass of the substance can be heated and added to water of known mass and initial temperature. Since the specific heat capacity of water is known ( C s,water =4.184J/(g⋅ ∘ C)) , the amount of heat transferred to the water can be calculated by measuring the final temperature of the mixture at thermal...
Under constant-volume conditions, 3100 J of heat is added to 1.9 moles of an ideal gas. As a result, the temperature of the gas increases by 78.5 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.