How much heat is needed to raise the temperature of 50.0 g of water from 4.5 ⁰C
to 83.0 ⁰C?

Taking into account the definition of calorimetry, the heat needed to raise the temperature of 50.0 g of water from 4.5 ⁰C  to   83.0 ⁰C is 16,406.5 J.

Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.

Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).

In this way, between heat and temperature there is a direct proportional relationship. The constant of proportionality depends on the substance that constitutes the body and its mass, and is the product of the specific heat by the mass of the body.

So, the equation that allows to calculate heat exchanges is:

Q = c× m× ΔT

where Q is the heat exchanged by a body of mass m, made up of a specific heat substance c and where ΔT is the temperature variation.

In this case, you know:

Replacing in the expression to calculate heat exchanges:

Q= 4.18 × 50 g× 78.5 C

Solving:

Q= 16,406.5 J

The heat needed to raise the temperature of 50.0 g of water from 4.5 ⁰C  to   83.0 ⁰C is 16,406.5 J.

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The heat  needed to raise the temperature of 50.0 g of water from 4.5 ⁰C

to   83.0 ⁰C is 16.46KJ

Explanation:

To solve the problem,

we need the value of the water and its given by,

C=4.18 × J/ g  ∘ C

To increase the temperature we need  m grams of water by n ∘ C

And the formula for the heat is given by, heat= m × n ×specific

heat

q = m ⋅ c . Δ T

where q denotes the heat absorbed

m denotes the mass sample

c denotes the specific heat

Δ T denotes the change in the temperature

Based on the data it is written as,

q= 50.0 g . 4.18  J /  g  ∘ C  (83.0-4.5) ∘ C

Simplifying the equation we get,

q=16406.5 J

Express it in the form of significant figure

16406.5 J . 1 KJ / 10^ 3 J

Solving the equation we get

16.46KJ

The heat  needed to raise the temperature of 50.0 g of water from 4.5 ⁰C

to   83.0 ⁰C is 16.46 KJ

the ideal gas law equation is as follows

pv = nrt

where p - pressure

v - volume

n - number of moles

r - universal gas constant

t - temperature

so if the pressure, volume and temperature are already known

we are left with n and r

since r is the universal gas constant that has a known fixed value then r too is known

so we are left with 'n'

once we know temperature volume and pressure

we can find the number of moles of gas present using the ideal gas law equation

this is not my own answer, this is an answer for the same question by the user blahblahmali. i do not claim ownership of this account.