# Cooling rates for Hydrogen and Neon gas

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## Homework Statement

1 mole of Hydrogen gas at 300 Kelvin is in a thin walled copper container vol 22.4 liters
surface area A = .476 M^2
In vessel #2 , 1 mole of Neon gas also 300 Kevin
The specific heat of H2= 5 cal/mole (K) Thermal conductivity (k) H2 = .0433 cal/sec. converts to .00866 deg K /sec
Specific heat Neon = 3 cal/mole (K) Thermal conductivity (k) Neon = .0116 cal/sec
converts to .0038 deg K/sec.
The surroundings are 100deg Kevin
How mant seconds for the gases to cool to 120 deg kelvin

## Homework Equations

Since k is from Q/t = -kA (T2-T1)/L where T2 is fixed Im applying k to Newtons law of
cooling: T(t) = Tsurr + (Tvessal - T surr ) e^-kt

## The Attempt at a Solution

For H2: 120K (t) = 100K + 200K e^-.00866t
2.3 = .00866 t t= 265 sec with kA t= 565 sec

for Neon 2.3=.0038t t= 605 sec with kA t =1292 sec

## The Attempt at a Solution

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Gold Member

## Homework Statement

1 mole of Hydrogen gas at 300 Kelvin is in a thin walled copper container vol 22.4 liters
surface area A = .476 M^2
In vessel #2 , 1 mole of Neon gas also 300 Kevin
The specific heat of H2= 5 cal/mole (K) Thermal conductivity (k) H2 = .0433 cal/sec. converts to .00866 deg K /sec
Specific heat Neon = 3 cal/mole (K) Thermal conductivity (k) Neon = .0116 cal/sec
converts to .0038 deg K/sec.
The surroundings are 100deg Kevin
How mant seconds for the gases to cool to 120 deg kelvin

## Homework Equations

Since k is from Q/t = -kA (T2-T1)/L where T2 is fixed Im applying k to Newtons law of
cooling: T(t) = Tsurr + (Tvessal - T surr ) e^-kt

## The Attempt at a Solution

For H2: 120K (t) = 100K + 200K e^-.00866t
2.3 = .00866 t t= 265 sec with kA t= 565 sec

for Neon 2.3=.0038t t= 605 sec with kA t =1292 sec

## The Attempt at a Solution

If converting k , the thermal conductivity, to Kevin/sec by way of dividing by the specific
heat was incorrect then this is a rework with k in cal/sec from table:
For Hydrogen, (t) 2.3 = .0433t t= 53sec
For Neon , (t) 2.3 = .0116t t=198sec

If this is not correct I would like to see someone work it out from the original problem