Heat capacities Definition and 28 Threads

Homework Statement:: I am trying to understand a formula given in our book for determining molar heat capacity of an ideal gas under different thermodynamic processes using a single formula, but it is confusing. The exact formula for different processes is in the screenshots below. Can someone...

I worked on a lab experiment that was meant to measure heat capacity but left me with some other questions. The students measured the mass of a cup of liquid nitrogen as it boiled off, recording mass vs time. Then they drop a solid object into the bath, one experiment with a small bit iron...

Homework Statement 117 J of energy is supplied as heat to 2.00 moles of an ideal gas at constant pressure, the temperature rises by 2.00 K. Calculate the molar heat capacity at constant pressure C_p,m and the molar heat capacity at constant volume C_v,m for the gas. Is the gas monatomic or...

Homework Statement Find the expression for c_p - c_v for a van-der-waals gas, with the equation of state \Bigg{(}p+\dfrac{a}{V^2}\Bigg{)}(V-b)=RT Homework EquationsThe Attempt at a Solution Basically I've proved c_p - c_v = \Bigg{[} p + \Bigg{(}\dfrac{\partial E}{\partial V}\Bigg{)}_T...

Homework Statement The constant-volume heat capacity of a particular simple system is c_v = AT^3 where A is a constant. In addition the equation of state is known to be of the form (v-v_0)p = B(T) where B(T) is an unspecified function of T. Evaluate the permissible functional form of B(T)...

Hello all, I am taking a thermodynamics course and unfortunately my professor is not very instructive. I have attended every class and I still feel lost. I was wondering how it is possible to find heat capacity if both the pressure and the volume are changing? I was under the impression that...

Homework Statement Consider a thermally insulated resistor with resistance R=20 Ω and mass m=5.0 g. The resistor is made of a material with specific heat capacity c=850 J/(g-K) and carries a current of 2.0 A for a time period of 1.0 s. a) Calculate the increase in the temperature of the...

Hi Guys I'm new the PF and hope I'm posting I the correct place, apologies to admin if not ;-). I'm working on a project at home and maths is not my strong suit. I have an equation that I need to complete and involves converting thermal heat capacity in water into electric power. From what I...

Hi all, I'm working through a derivation of the general relationship between Cp and Cv and there's one point which is confusing me. I understand that and and that this implies the following: but isn't this equal to 0? Shouldn't the two partial derivatives on the right...

Homework Statement Given the equation of state ##V(P,T)=V_1\cdot exp(\frac{T}{T_1}-\frac{P}{P_1})## where ##V_1\;,T_1\;,P_1## are constants: a. derive an equivalent equation ##P(V,T)##; b. given ##C_V=DT^3## where D is a const, calculate the entropy of the system ##s(V,T)## up to a const; c...

From relation C_p-C_v=[P+(\frac{\partial U}{\partial V})_T](\frac{\partial V}{\partial T})_P In case of water ##(\frac{\partial V}{\partial T})_P<0## so ##C_p<C_v##? Right?

Homework Statement A quantity of water in a beaker of negligible thermal capacity is cooled to a few degrees below freezing point. The beaker is then placed in a warm room, and the times recorded at which it is at various temperatures as it gradually warms. The observations were...

Hi Admin, please allow me to post this here: The General Formula for Specific Heat Capacity is: C(Total) = C(electron)+C(phonon) C(electron) = aT where a is the sommerfield constant. C(phonon) = bT^3 this time i don't know what is b (some constant) so my problem is, how can i determine b...

Please help me qualitatively in the following points : 1) If in a system(consider a cylinder) fixed with a piston , if the piston is moved suddenly then how can a process be adiabatic. 2) I understood that the process would be irreversible but, if the process is adiabatic then is the relation...

Hey having a bit of trouble with this one. I really don't know how to start. Think I just simply don't have the right equations or I'm using the wrong units. Hopefully you guys can help me. Homework Statement Find the molar mass and the number of degrees of freedom of molecules in a gas with...

Hi everybody, I have the following doubt. We know that for a thermodynamic system the following equality holds: $$ C_P-C_V=-T\frac{\left[\left(\frac{\partial P}{\partial T}\right)_V\right]^2}{\left(\frac{\partial P}{\partial V}\right)_T} $$ Now, the mechanical stability of the system...

Can someone please tell me what does the symbol H and what does the symbol U represent in these equations: http://www.taftan.com/thermodynamics/CP.HTM"][/PLAIN] http://www.taftan.com/thermodynamics/CP.HTM

Homework Statement Two somewhat related problems: 1. Using the expression for change in entropy of an ideal gas per mole: ΔS=CV+R ln(V) Calculate the change in entropy, change in Helmholtz Free Energy and change in Gibbs Free Energy when 1 mole of an ideal gas is compressed from 1 atm to 20...

I am confused why the heat capacity at constant pressure can be different from the heat capacity at constant volume. I am also having difficulties absorbing the material regarding the kinetic theory of gases, such as keeping all the ΔE_int changes with what processes etc. Why can adiabatic...

Homework Statement A cylinder contains 0.2mol of Helium at 30 degrees C and is heated different ways. How much heat is needed to raise the temperature to 70C while keeping thevolume constant? Homework Equations dQ=dU+dT nCpdT=nCvdT+nRdT The Attempt at a Solution What I am...

Hi all, I'm working with the heat capacities definition and I have got a confusion. I don't understand why we can express them like Cp = T(∂S/∂T)p Cv = T(∂S/∂T)v I know that Cp=(dQ/dT)p = (∂H/∂T)p with H equal to TdS + VdP and Cv=(dQ/dT)v = (∂U/∂T)v with U equal to TdS + PdV, My...

I have the answer to this question but I'm finding it hard making sense of it... Q5) Dervive a relationship relating Cp-Cv to the isothermal compressibility (∂p/∂V)T and the coefficient of thermal expansion (∂V/∂T)p. Hint: consider the intensive entropy S as a function of T and V. So I've...

Homework Statement To find the ratio of the specific heat capacities of air (γ). Homework Equations PVγ=constant The Attempt at a Solution I performed the experiment a number of times to get an average for γ The experiment consisted of a container with release valve, a hand...

Homework Statement 1 gram of Hydrogen H_2 and 1 gram of Helium He are put together into a container of 10 L in volume and at a temperature of 27°C. (a) Find the pressure (b) Find the molar specific heat capacities C_v and C_p, as well as \gamma = \frac{C_p}{C_v} of this gas mixture...

For an isochoric process, dV = 0 therefore dW=0 So from 1st of Thermodynamics, dQ = dU + 0 or, n*Cp*dT = n*Cv*dT (Cp and Cv denote molar heat capacities of the gas at const pressure and volume resp.) therefore we get Cp = Cv .(how can this be possible once we know Cp - Cv = R ?)

Hi, my task is to calculate the ratio (gamma) between the specific heats of a gas (Cp and Cv). The only information I have is a table of data for the pressures and volumes of the gas at different temperatures. I don't know if its monatomic, diatomic etc. (it's a later task to determine this)...

Homework Statement a. Consider an ideal gas being heated at constant volume, and let Cv be the gas's molar heat capacity at constant volume. If the gas's infinitesimal change in temperature is dT, find the infinitesimal change in internal energy dU of n moles of gas. Express the...

Homework Statement This question refers to Pathria's Statistical Mechanics textbook. In this problem, there is the equation: \frac{C_P}{C_V} = \frac{\left(\partial z /\partial T \right)_P}{\left(\partial z /\partial T\right)_{\nu}} where z is the fugacity and \nu is the volume per...