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I just need help to solve a problem:

Show that (∂E/∂V)β, N + β(∂p/∂β)N, V = - p

PS: There is a bar over E and over p (this in both sides) - meaning that is an average.
The temperature of a 46.4 g sample of a metal is raised from 21.3 degrees celsius to 55.9 degrees celcius when 400.6 cal of heat are added. The specifc heat capacity of the sample is what in cal/g*oC.
a closed vesswl having capacity200ml is filled with hydrogen gas STP. calculate:
number of moles of hydrogen gas filled in the vessel
pressure of hydrogen gas in the vessel ai 273 degree c
root mean square velocity of hydrogen gas at STP
the value of Cp and Cv for hydrogen gas
Find difference between the mean square speeds of hydrogen and oxygen molecules at N.T.P. Take molecular weight of hydrogen and oxygen as 2 and 32.
Two vesseles having volume of 5 litres and 3 litres contain air at pressure of 3 atmosphere and 7 atmospheres resp. What will be the resultant presure when they are connected together with a small tube? Assume temperature remains constant throughout.
904.5 g of ice is melted at a temperature of
29◦F.
Find the change in entropy.
Answer in units of J/K.
1. An unbreakable meteorological balloon is released from the ground.Ground level pressure is 98.5 KPa and the temperature is 18.0 Celsius. The balloon contains 74.0 liters of Hydrogen gas. As the balloon soars up, the pressure drops to 27.0 KPa. What is the new volume of the balloon, assuming no temperature change?
2. Re-read question 1, but considering in the real world when you go up in altitude the temperature does change. what is the actual volume of the meteorological balloon if the temp also drops 79.0 celsius from its original temperature?
state the steady flow energy equation and mention all the variables used and their corresponding standard si unite
the temperature at which the solid and liquid phases are in equilibrium is?

a) boiling point

b) melting point

c) freezing point

d) equilibrium point
Do conduction phenomenon occur in air ?
If not what is responsible for the experiment of action of point in which air molecules get charged and are repelled as a result strong electric wind develops which blow a candle flame kept aside in experiment ?
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