A piece of a newly synthesized material of mass 25.0 g at 80.0◦C is placed in a calorimeter containing 100.0 g of water at 20.0◦C. If the final temperature of the system is 24.0◦C, what is the specific heat capacity of this new material? 1. 1.20 J/g ◦C 2. 7.46 J/g ◦C 3. 4.76 J/g ◦C 4. 0.30 J/g ◦C 5. 0.84 J/g ◦C

1.Cp₁ = 1.2 J/g.⁰C

Explanation:

For new material:

m₁  = 25 g

T₁ = 80⁰C

specific heat of water = Cp₁

For water :

m₂ = 100 g

T₂ = 20⁰C

The final temperature T=24⁰C

We know that specific heat of water Cp₂ = 4.187 kJ/kg.K

The heat lost new material = Heat gain by Water

m₁ Cp₁ ( T₁ - T ) = m₂ Cp₂ (T- T₂)

25 x Cp₁ (80- 24 ) = 100 x 4.817 (24 - 20 )

Cp₁  x 56 = 4 x 4.187 x 4

Cp₁ = 1.19 kJ/kg.K

Cp₁ = 1.2 J/g.⁰C

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emily ruth's annual premium is $1058.50

step-by-step explanation:

emily ruth is a female of 27 years age purchasing 20 year endowment insurance with face value $25000.

from the given table,

for females, the age of a male 3 years younger should be used.

so, we have to check for 24 year male for 20 year endowment.

it is 42.34 for every $1000 face value.

for a face value of $25000,

it is 25 * 42.34 = $1058.50

∴ emily ruth's annual premium is $1058.50