Why don't units have match for specific heat and mass

[Perseverence]

Homework Statement

A problem will ask for an amount of substance in kilograms to be raised to a certain temperature and the specific heat be given in J/g*K. The amount of substance is not required to be converted to grams to match the units in the specific heat to get the correct amount of joules needed. Is that correct? Why is that? It doesn't make sense to me.

Homework Equations

Q=mc(delta)T

The Attempt at a Solution

The units of mass for m and for c don't have to match. This doesn't make sense to me.[/B]

 

[Perseverence]

I'm pretty sure I've also seen this was units of temperature not matching the units in the specific heat maybe in kelvin and the amount of temperature change will be in Celsius, yet nothing has to be converted to get the temperature units to match and to get the right answer

 

[Perseverence]

specifically 0.2 kg of hydrogen is heated from 250 K to 280 K with specific heat of hydrogen gas being 14.3 J/g *K.

86 joules is the amount of heat needed to change the temperature the amount requested. This would only occur with mass of hydrogen and specific heat of hydrogen being in different units of mass

 

[NascentOxygen]

I'm pretty sure I've also seen this was units of temperature not matching the units in the specific heat maybe in kelvin and the amount of temperature change will be in Celsius, yet nothing has to be converted to get the temperature units to match and to get the right answer

When a problem involves a change of temperature, no explicit conversion °C↔K is needed because a change of 1°C is the same as a change of 1 K. Their scales on any thermometer are the same, the scales only differ in which mark they call zero.

 

[Perseverence]

Okay that makes sense for temperature. Why doesn't Mass have to be converted to match?

 

[NascentOxygen]

specifically 0.2 kg of hydrogen is heated from 250 K to 280 K with specific heat of hydrogen gas being 14.3 J/g *K.

86 joules is the amount of heat needed to change the temperature the amount requested. This would only occur with mass of hydrogen and specific heat of hydrogen being in different units of mass

You wish to raise 200g by 30 degrees, each gram requiring 14.3 J per degree. Are you missing some powers of 10 in your answer?

 

[Perseverence]

You wish to raise 200g by 30 degrees, each gram requiring 14.3 J per degree. Are you missing some powers of 10 in your answer?

Is 86 joules not the correct answer? That is the answer that is given by the book

 

[Perseverence]

Please let me know if the answer in the book is incorrect. That would explain a lot to me. It's very frustrating because I've seen this error more than once and it's affected the way I've learned how to solve this kind of problem, but I'm happy to relearn it the correct way if the book is indeed wrong

 

[NascentOxygen]

Is 86 joules not the correct answer? That is the answer that is given by the book

Either the question or the answer is wrong. What do you think the answer should be?

 

[Perseverence]

I think the answer should be 85800 J

 

[NascentOxygen]

A problem will ask for an amount of substance in kilograms to be raised to a certain temperature and the specific heat be given in J/g*K. The amount of substance is not required to be converted to grams to match the units in the specific heat to get the correct amount of joules needed. Is that correct?

No, it's not correct. You can experiment with this using a pencil and a piece of paper. ☺

If specific heat is given as, say, 23.6 J/g°C
what value would it be when expressed as kJ/kg°C?

 

[Perseverence]

This is an image of the solution in the book

 

[NascentOxygen]

This is an image of the solution in the book

It seems that the typist omitted the k in the answer. An easy mistake to make.

 

[Perseverence]

Okay. Thank you for confirming that it's a mistake. It's actually amuch bigger mistakes and then just a missing k. The original question was multiple choice with the possible answers being 46 joules 72 tools 56 joules 35 joules in 86 joules.

 

[Perseverence]

Thank you so much for helping! You saved me hours of misery . Textbook mistakes when you are self teaching are absolutely devastating.

 

[Perseverence]

One key fact I may have left out that may make a difference. The question mentions that .2 kg of hydrogen gas is in a rigid container. Would that make any difference in the answer?

 

[NascentOxygen]

Okay. Thank you for confirming that it's a mistake. It's actually amuch bigger mistakes and then just a missing k. The original question was multiple choice with the possible answers being 46 joules 72 tools 56 joules 35 joules in 86 joules.

It's more likely the oversight is in the question and not in each of the 4 answer options. ☺ The answer of 86 J would be correct had the question involved 0.2 grams, not 0.2 kg.

 

[NascentOxygen]

hydrogen gas is in a rigid container. Would that make any difference in the answer?

If the container is allowed to expand as the contents are heated the problem becomes more complicated.

 

[Perseverence]

Thank you. Your answers makes so much sense. So my answer was correct if I solve the problem the way it is written. 85800 J is the correct answer. I just want to confirm, because you had mentioned that it was the wrong answer before.

 

[NascentOxygen]

85800 J is the correct answer.

That's correct.

 

[Perseverence]

Wonderful! Thank you for the confirmation!

 

[CWatters]

In case it's not obvious by now... The units _do_ matter. It's also common for the question to ask for an answer in Kg and for the constant to be given in other units eg grams.