Thermodynamics pressure-temperature-volume problems

[Termodinamica]

Homework Statement

When the volume of a gas is reduced with fp% and the gas is heaten with ΔT K, the pressure of it grows with fp%.Find initial temperature Ti.
Application: fv%= 20%; ΔT 12 K; fp% = 30%


2.A aluminium calorimeter with the mass m1 contains the mass m2 of water heated at T1.In the water from calorimeter is inserted a body of lead(Pb) at mass m3 at the temperature of T3 (>T1).The termic equilibrum is set at the temperature T.We have the specific heats c1 and c2 of the aluminium and of the water.Find the specific heat c3 of the lead.
Application: m1 = 41,6 g; m2 = 0,232 kg; T1= 288 K; m3 = 0,1 kg; T3 = 373 K; T =289K; c1 = 920 J/(kg * K); c2 = 4180 J/(kg * K).

Homework Equations

At 1 the T1 = 300k and at 2 c3 = 120 J(kg *K)

The Attempt at a Solution

 

[Richard R Richard]

In the equilibrium of temperature between the calorimeter and lead, you have that the heat given by the lead when reducing its temperature, is the same heat that the water and the aluminum calorimeter receive to increase its initial temperature until the equilibrium temperature.
in formulas

$$Q = m_{3}Ce_{Pb} (T_{3}-T) = m_{1}Ce_{H2O} (T_{1}-T) + m_{2}Ce_{Al} (T_{1}-T)$$
from the last equality, clear and calculate $$Ce_ {Pb}$$

 

[Charles Link]

The first problem is solved very easily with $P_1 V_1=n_1 RT_1$ , and writing $PV=nRT$ again with the conditions that are applied.

 

[Charles Link]

In the equilibrium of temperature between the calorimeter and lead, you have that the heat given by the lead when reducing its temperature, is the same heat that the water and the aluminum calorimeter receive to increase its initial temperature until the equilibrium temperature.
in formulas

$$Q = m_{3}Ce_{Pb} (T_{3}-T) = m_{1}Ce_{H2O} (T_{1}-T) + m_{2}Ce_{Al} (T_{1}-T)$$
from the last equality, clear and calculate $$Ce_ {Pb}$$

I think on the right side you need $T-T_1$. Otherwise, very good.
Meanwhile, this is a very old homework. (9 years old). I don't think the OP is needing a response anymore.

 

[Richard R Richard]

Hello, I am new to the forum, the problem is easy and I answered.
you are right about reversing signs on the right side.
I had started from
$$\displaystyle{\sum Q_i=\sum m_iCe_i(T_i-T)=0}$$
conservation law...
but copy and paste, forget to reverse the signs , sorry, thank you.

 

[berkeman]

Hello, I am new to the forum, the problem is easy and I answered.

Keep in mind that it was okay for you to answer this homework question because it is 9 years old. In general, we do not provide answers to homework questions, especially those where the OP showed little effort.

We give hints, ask questions, find mistakes, etc. But we don't do a student's homework for them here. Welcome to PhysicsForums!