A mass m of water is heated reversibly from temperature t1...

A mass m of water is heated reversibly from temperature T1 to T2 at a constant pressure of P. In this problem, we are going to determine an expression for the change in entropy, ΔS. Assume we can heat the given water infinitesimally slowly so that the process is reversible. Therefore, heat in any infinitesimal step is given by the following: dQ = mc dT, where c is the specific heat and is constant. Part (a) ✔ Write an expression for the change in entropy ΔS for the system. ✔ Correct! Part (b) Calculate the change in entropy in cal/K for a sample of water with mass m = 2.6 kg and changing temperature from T1 = 17.2°C to T2 = (17.2+10)°C. The specific heat c of water is 1,000 cal/kg/K.

Transcript

00:01 Now here we look at entropy change, right? we look at water, intrepid change.

00:09 Now imagine you have quantum water, right? initial at 10 degrees.

00:15 So suppose initially temperature has the water has temperature, which is as a ti initially, is 10 celsius degrees.

00:25 And then it's brought into contact with a heat reserver, which has temperature, which is tf equals 90, 90 degrees, right? and of course, it's going to absorb a heat from this heat reservoir, right? the heat reserve has a temperature, which is fixed, constant temperature, right? so, but the temperature of the water is going to rise.

00:45 So what's intrepid change of the water? so let's say intrepid change of the water, okay? and this, of course, is given by, you know, t, i, t, f, and, you know, the specific heat of water, which i call the cv, and divided by temperature t, and divide and times d t right so um that's what you get so you will get this to be a cv log t f over t i right so that would be the intrepid change um of the water right and of course by the way you have to make sure this is get in calvin so i make sure this is is important in cavans so that's actually 283 caverns and this is actually, you know, it's 263 kelvin, sorry, 363 calvins, yeah, cabins.

01:39 So you need to plug this kevin, the temperatures and caverns into this formula like to calculate the result.

01:45 So that's the intrope change of what.

01:46 How about the intrepichity change of, what is the intubary change of the, of the hit reserve, right? reserver, the temperature change, of course, is because the temperature of the reserve does not change.

02:00 So it's simply given by a tf, right, which is 363 kherns, and all the heat are the gives.

02:07 So that will be minus time.

02:09 So that would be cv times tf minus tri, right? that's the answer...

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