When a system is heated, heat is by the system. the amount of heat added is given a sign. when a system is cooled, heat is by the system. the amount of heat is given a sign. if a gas expands, it must push the surrounding atmosphere away. thus, work is done the system and is given a sign. if a gas is compressed, then work is done the system. this work is given a sign.

First of all, we need to write the First Law of thermodynamics assigning the correct sign convention:

where

is the change in internal energy of the system

Q is the heat absorbed/released

W is the work done

and the signs are assigned based on whether there is an increase in the internal energy or not. Therefore:

Q is positive if it is absorbed by the system (because internal energy increases)

Q is negative if it is released by the system (because internal energy decreases)

W is negative if it is done by the system on the surrounding (because internal energy decreases)

W is positive if it is done by the surrounding on the system (because internal energy increases)

Using these definitions, we can now fill the text of the question:

When a system is heated, heat is ABSORBED by the system. The amount of heat added is given a POSITIVE sign. When a system is cooled, heat is RELEASED by the system. The amount of heat is given a NEGATIVE sign. If a gas expands, it must push the surrounding atmosphere away. Thus, work is done BY the system and is given a NEGATIVE sign. If a gas is compressed, then work is done ON the system. This work is given a POSITIVE sign.

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